km.ci/0000755000176200001440000000000014223277412011257 5ustar liggesuserskm.ci/NAMESPACE0000644000176200001440000000052214223001017012457 0ustar liggesusers# Generated by roxygen2: do not edit by hand export(critical.value.hall.90) export(critical.value.hall.95) export(critical.value.hall.99) export(critical.value.nair.90) export(critical.value.nair.95) export(km.ci) import(survival) importFrom(stats,qchisq) importFrom(stats,qnorm) importFrom(utils,data) importFrom(utils,globalVariables) km.ci/data/0000755000176200001440000000000014223000316012153 5ustar liggesuserskm.ci/data/rectum.dat.rda0000755000176200001440000000306014223001177014721 0ustar liggesusers[lUJJҦ:^h;gPv&*}SDԖ]X CB&HF}@XxQ4DcLhbx:`@0@ =51AΜ-FWq+E"H~Nn$7/fɉG 帞 ] k:H7#4=zdDbc^0%Nۡ: d4K$zn^ oܦݐJ5rKoHЙ+p\발^D̯H׫_ MƱhwAsa,!M:. 嶃-0 =oX`(:#H*:CD=(|D*_dMfz%6yّ7auyqU8^:[ cDbY'c1c>NeR#d͕U``YeEO=Pb|ϗ~ ǷiPqw#ܲl :|)Q'f⺼/U}\vT?p<r]Z﷜u(i㼛Xp|̨\t6^Sɲ998V^ҖL/?Bshky-1\ïn' 5)<Ḷ~!]5_U8^.K*z7հ|BZyP9C3?&x ~>Պ|&wjݪR>p~EJz^ 9{GgWKuS[[JuǪ PPK *Tck4QdP$(2)()r(r)("C!d2 A C!0000000000ɰȰȰȰȰȰȰȰȰȰȰɰɰɰɰɰɰɰɰɰppppppppppppppppppppg45qhp(84989t8t98d``````````M&X k5`M&X3Y3Y3Y3Y3Y3Y3Y3Y3Y3YXXXXXXXXXXYYYYYYYYYYsXsXsXsXsXsXsXsXsXsXsYsYsYsYsYsYsYsYsYsYXXXXXXXXXXYYYYYYYYYDY",|>K%"{َ^GwMGamOIkFkm.ci/man/0000755000176200001440000000000014223000316012015 5ustar liggesuserskm.ci/man/km.ci.Rd0000644000176200001440000000614314223000316013311 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/km.ci.R \name{km.ci} \alias{km.ci} \title{Confidence Intervals for the Kaplan-Meier Estimator.} \usage{ km.ci(survi, conf.level = 0.95, tl = NA, tu = NA, method = "rothman") } \arguments{ \item{survi}{A survival object for which the new confidence limits should be computed. This can be built using the "Surv" and the "survfit" function in the R package "survival". "km.ci" modifies the confidence limits in this object.} \item{conf.level}{The level for a two-sided confidence interval on the survival curve. Default is 0.95.} \item{tl}{The lower time boundary for the simultaneous confidence limits. If it is missing the smallest event time is used.} \item{tu}{The upper time boundary for the simultaneous confidence limits. If it is missing the largest event time is used.} \item{method}{One of '"peto"', '"linear"', '"log"', "loglog"', '"rothman"', "grunkemeier"', '"hall-wellner"', '"loghall"', "epband"', "logep"} } \value{ a 'survfit' object; see the help on 'survfit.object' for details. } \description{ Computes pointwise and simultaneous confidence intervals for the Kaplan-Meier estimator. } \details{ A simulation study showed, that three confidence intervals produce satisfying confidence limits. One is the "loglog" confidence interval, an interval which is based on the log of the hazard. The other competitive confidence concept was introduced by Rothman (1978) and is using the assumption that the survival estimator follows a binomial distribution. Another good confidence concept was invented by Thomas and Grunkemeier (1975) and is derived by minimizing the likelihood function under certain constraints. Special thanks goes to Robert Gentleman for providing code for the confidence interval by Thomas and Grunkemeier. The confidence interval using Peto's variance can not be recommended since it yields confidence limits outside the admissible range [0;1] as well as the "linear" and the "log" (which is based on the logarithm of S(t)). The function can produce simultaneous confidence bands, too. The Hall-Wellner band (1980) and the Equal Precision band by Nair (1984) together with their log-transformed counterpart. From all simultaneous confidence intervals only the log-transformed Equal Precision "logep" band can be recommended. The limits are computed according to the statistical tables in Klein and Moeschberger (2002). } \examples{ require(survival) data(rectum.dat) # fit a Kaplan-Meier and plot it fit <- survfit(Surv(time, status) ~ 1, data=rectum.dat) plot(fit) fit2 <- km.ci(fit) plot(fit2) } \references{ Strobl, R., Dirschedl, P. and Mansmann, U.. Comparison of simultaneous and pointwise confidence intervals for survival functions. (2005, submitted to Biom. J.). } \seealso{ \code{\link[survival]{survfit}}, \code{\link[survival]{print.survfit}}, \code{\link[survival]{plot.survfit}}, \code{\link[survival]{lines.survfit}}, \code{\link[survival]{summary.survfit}}, \code{\link[survival]{survfit.object}}, \code{\link[survival]{coxph}}, \code{\link[survival]{Surv}}, \code{\link[survival]{strata}}. } \author{ Strobl, R. } \keyword{survival} km.ci/man/critical.value.nair.90.Rd0000644000176200001440000000065714222643020016404 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/km.ci-package.R \docType{data} \name{critical.value.nair.90} \alias{critical.value.nair.90} \title{Critical Values} \source{ Klein, Moeschberger (2002): Survival Analysis, Springer. } \description{ Critical values for the 90 \% equal precision band by Nair. } \details{ These values are taken from the book by Klein & Moeschberger. } \keyword{datasets} km.ci/man/critical.value.hall.95.Rd0000644000176200001440000000064314222643020016373 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/km.ci-package.R \docType{data} \name{critical.value.hall.95} \alias{critical.value.hall.95} \title{Critical Values} \source{ Klein, Moeschberger (2002): Survival Analysis, Springer } \description{ Critical values for the 95 \% Hall-Wellner band. } \details{ These values are taken from the book by Klein & Moeschberger. } \keyword{datasets} km.ci/man/rectum.dat.Rd0000644000176200001440000000151214222644060014362 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/km.ci-package.R \docType{data} \name{rectum.dat} \alias{rectum.dat} \title{Rectum carcinoma data set.} \format{ A data frame with 205 observations on the following 2 variables. \describe{ \item{time}{Time in months} \item{status}{Status at dropout} } } \source{ Merkel, Mansmann et al.(2001).The prognostic inhomogeneity in pT3 rectal carcinomas. Int J Colorectal Dis.16, 305--306. } \description{ The rectum data contains 205 persons from a study about the survival of patients with rectum carcinoma. Due to the severe course of disease the follow-up was almost perfect in these data and involves hardly any censoring and survivors. The data was used to analyze the behavior of the confidence intervals in data sets with low censoring rate. } \keyword{datasets} km.ci/man/critical.value.nair.99.Rd0000644000176200001440000000065714222643020016415 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/km.ci-package.R \docType{data} \name{critical.value.nair.99} \alias{critical.value.nair.99} \title{Critical Values} \source{ Klein, Moeschberger (2002): Survival Analysis, Springer. } \description{ Critical values for the 99 \% equal precision band by Nair. } \details{ These values are taken from the book by Klein & Moeschberger. } \keyword{datasets} km.ci/man/critical.value.nair.95.Rd0000644000176200001440000000065714222643020016411 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/km.ci-package.R \docType{data} \name{critical.value.nair.95} \alias{critical.value.nair.95} \title{Critical Values} \source{ Klein, Moeschberger (2002): Survival Analysis, Springer. } \description{ Critical values for the 95 \% equal precision band by Nair. } \details{ These values are taken from the book by Klein & Moeschberger. } \keyword{datasets} km.ci/man/critical.value.hall.90.Rd0000644000176200001440000000064414222643020016367 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/km.ci-package.R \docType{data} \name{critical.value.hall.90} \alias{critical.value.hall.90} \title{Critical Values} \source{ Klein, Moeschberger (2002): Survival Analysis, Springer. } \description{ Critical values for the 90 \% Hall-Wellner band. } \details{ These values are taken from the book by Klein & Moeschberger. } \keyword{datasets} km.ci/man/critical.value.hall.99.Rd0000644000176200001440000000064414222643020016400 0ustar liggesusers% Generated by roxygen2: do not edit by hand % Please edit documentation in R/km.ci-package.R \docType{data} \name{critical.value.hall.99} \alias{critical.value.hall.99} \title{Critical Values} \source{ Klein, Moeschberger (2002): Survival Analysis, Springer. } \description{ Critical values for the 99 \% Hall-Wellner band. } \details{ These values are taken from the book by Klein & Moeschberger. } \keyword{datasets} km.ci/DESCRIPTION0000755000176200001440000000133114223277412012766 0ustar liggesusersPackage: km.ci Type: Package Title: Confidence Intervals for the Kaplan-Meier Estimator Version: 0.5-6 Date: 2022-04-04 Author: Ralf Strobl Maintainer: Tobias Verbeke Depends: R (>= 3.5.0) Imports: stats, survival Description: Computes various confidence intervals for the Kaplan-Meier estimator, namely: Peto's CI, Rothman CI, CI's based on Greenwood's variance, Thomas and Grunkemeier CI and the simultaneous confidence bands by Nair and Hall and Wellner. License: GPL (>= 2) Encoding: UTF-8 Repository: CRAN RoxygenNote: 7.1.2 NeedsCompilation: no Packaged: 2022-04-05 08:49:03 UTC; tverbeke Date/Publication: 2022-04-06 11:52:42 UTC km.ci/R/0000755000176200001440000000000014223000703011443 5ustar liggesuserskm.ci/R/rothman.fun.R0000755000176200001440000000155314222643000014036 0ustar liggesusers#' @importFrom stats qnorm "rothman.fun" <- function(sfit,conf.level=0.95) { if(conf.level < 0 || conf.level > 1) stop("confidence level must be between 0 and 1") else s.t <- sfit$surv zalpha<-qnorm( 1 - (1-conf.level)/2) tvec<-sfit$n.event/(sfit$n.risk*(sfit$n.risk - sfit$n.event)) tv2<-cumsum(tvec) var.st <- tv2*s.t^2 n.null <- s.t*(1-s.t)/var.st roth.upper <- n.null/(n.null+zalpha^2)*(s.t+zalpha^2/(2*n.null)+zalpha*sqrt(var.st+zalpha^2/(4*n.null^2))) roth.lower <- n.null/(n.null+zalpha^2)*(s.t+zalpha^2/(2*n.null)-zalpha*sqrt(var.st+zalpha^2/(4*n.null^2))) sfit <- sfit roth.upper[is.na(roth.upper)] <- 1 roth.lower[is.na(roth.lower)] <- 1 sfit$upper <- roth.upper sfit$lower <- roth.lower return(list(rothman.upper=roth.upper,rothman.lower=roth.lower,surv.object=sfit)) } km.ci/R/a.up.low.fun.R0000755000176200001440000000232114223000316014021 0ustar liggesusers#' @import survival "a.up.low.fun" <- function(survi, tl, tu) { # Calculates the indices used to derive the critical value # determining a Hall-Wellner band. It takes the a survfit object # and returns the values belonging to the two timepoints # and a matrix with time, the Kaplan-Meier estimator, the sigmas # (the sum in Greenwood's formula) and the std. error. # t1 should be at least the smallest time, tu the smaller or equal # than the highest time. survi <- survi n <- survi$n time <- survi$time kap.mei <- survi$surv indices <- (1:length(time))[survi$n.event>0] n.risk <- survi$n.risk n.event <- survi$n.event a <- n.event/(n.risk*(n.risk-n.event)) a <- cumsum(a) var.st <- kap.mei^2*a std.err <- sqrt(var.st) sigma <- var.st/kap.mei^2 index.low <- max((1:length(time))[(time-tl)<=0]) index.up <- max((1:length(time))[(time-tu)<=0]) sigma.low <- sigma[index.low] sigma.up <- sigma[index.up] al <- n*sigma.low/(1+n*sigma.low) au <- n*sigma.up/(1+n*sigma.up) return(list(a.low=al,a.up=au,sigma.mat=cbind(time,kap.mei,sigma,std.err) ,start=index.low,end=index.up)) } km.ci/R/km.ci-package.R0000644000176200001440000000501714222644056014201 0ustar liggesusers #' Critical Values #' #' Critical values for the 90 \% Hall-Wellner band. #' #' These values are taken from the book by Klein & Moeschberger. #' #' @name critical.value.hall.90 #' @docType data #' @source Klein, Moeschberger (2002): Survival Analysis, Springer. #' @keywords datasets NULL #' Critical Values #' #' Critical values for the 95 \% Hall-Wellner band. #' #' These values are taken from the book by Klein & Moeschberger. #' #' @name critical.value.hall.95 #' @docType data #' @source Klein, Moeschberger (2002): Survival Analysis, Springer #' @keywords datasets NULL #' Critical Values #' #' Critical values for the 99 \% Hall-Wellner band. #' #' These values are taken from the book by Klein & Moeschberger. #' #' @name critical.value.hall.99 #' @docType data #' @source Klein, Moeschberger (2002): Survival Analysis, Springer. #' @keywords datasets NULL #' Critical Values #' #' Critical values for the 90 \% equal precision band by Nair. #' #' These values are taken from the book by Klein & Moeschberger. #' #' @name critical.value.nair.90 #' @docType data #' @source Klein, Moeschberger (2002): Survival Analysis, Springer. #' @keywords datasets NULL #' Critical Values #' #' Critical values for the 95 \% equal precision band by Nair. #' #' These values are taken from the book by Klein & Moeschberger. #' #' @name critical.value.nair.95 #' @docType data #' @source Klein, Moeschberger (2002): Survival Analysis, Springer. #' @keywords datasets NULL #' Critical Values #' #' Critical values for the 99 \% equal precision band by Nair. #' #' These values are taken from the book by Klein & Moeschberger. #' #' @name critical.value.nair.99 #' @docType data #' @source Klein, Moeschberger (2002): Survival Analysis, Springer. #' @keywords datasets NULL #' Rectum carcinoma data set. #' #' The rectum data contains 205 persons from a study about the survival of #' patients with rectum carcinoma. Due to the severe course of disease the #' follow-up was almost perfect in these data and involves hardly any censoring #' and survivors. The data was used to analyze the behavior of the confidence #' intervals in data sets with low censoring rate. #' #' #' @name rectum.dat #' @docType data #' @format A data frame with 205 observations on the following 2 variables. #' \describe{ \item{time}{Time in months} \item{status}{Status #' at dropout} } #' @source Merkel, Mansmann et al.(2001).The prognostic inhomogeneity in pT3 #' rectal carcinomas. Int J Colorectal Dis.16, 305--306. #' @keywords datasets NULL km.ci/R/modify.surv.fun.R0000755000176200001440000000122013351150552014651 0ustar liggesusers"modify.surv.fun" <- function(survi,start,end,method) { # This function simply modifys an survival object # and cuts off the ends where no upper and lower # boundary is calculated survi <- survi survi$time <- survi$time[start:end] survi$n.risk <- survi$n.risk[start:end] survi$n.event <- survi$n.event[start:end] survi$surv <- survi$surv[start:end] survi$std.err <- survi$std.err[start:end] survi$upper <- survi$upper[start:end] #survi$upper[survi$upper>1] <- 1 survi$lower <- survi$lower[start:end] #survi$lower[survi$lower<0] <- 0 survi$conf.type <- method return(survi) } km.ci/R/comp.npci.R0000755000176200001440000000314114222644273013475 0ustar liggesusers#' @importFrom stats qnorm "comp.npci" <- function(sfit,conf.level=0.95, restrict=F) { if(!inherits(sfit,"survfit")) stop("need the output of survfit") if(conf.level < 0 || conf.level > 1) stop("confidence level must be between 0 and 1") else zalpha<-qnorm( 1 - (1-conf.level)/2) tvec<-sfit$n.event/(sfit$n.risk*(sfit$n.risk - sfit$n.event)) tv2<-cumsum(tvec) sqrt.tv2<-sqrt(tv2) peto.se<-sqrt.tv2/log(sfit$surv) gw.se<-sfit$surv * sqrt.tv2 gw.lower<-exp(log(sfit$surv)-zalpha*sqrt.tv2) gw.upper<-exp(log(sfit$surv)+zalpha*sqrt.tv2) #gw.upper<-ifelse(gw.upper>1,1,gw.upper) llog.lower<-sfit$surv^(exp(-zalpha*peto.se)) llog.upper<-sfit$surv^(exp(zalpha*peto.se)) linear.lower<-sfit$surv-zalpha*gw.se linear.upper<-sfit$surv+zalpha*gw.se binom.se<-sfit$surv * sqrt((1-sfit$surv)/(sfit$n.risk)) peto.lower<-sfit$surv - zalpha * binom.se peto.upper<-sfit$surv + zalpha * binom.se if( restrict) { gw.lower<-ifelse(gw.lower<0,0,gw.lower) gw.upper<-ifelse(gw.upper>1,1,gw.upper) llog.lower<-ifelse(llog.lower<0,0,llog.lower) llog.upper<-ifelse(llog.upper>1,1,llog.upper) peto.lower<-ifelse(peto.lower<0,0,peto.lower) peto.upper<-ifelse(peto.upper>1,1,peto.upper) linear.lower<-ifelse(linear.lower<0,0,linear.lower) linear.upper<-ifelse(linear.upper>1,1,linear.upper) } return(list(greenwood=list(lower=gw.lower,upper=gw.upper), loglog=list(lower=llog.lower,upper=llog.upper), peto=list(lower=peto.lower,upper=peto.upper), linear=list(lower=linear.lower,upper=linear.upper))) } km.ci/R/abweich.fun.R0000755000176200001440000000066013351150552013775 0ustar liggesusers"abweich.fun" <- function(matrix,k,n) { # Calculates the upper and lower derivation to the Kaplan-Meier estimator # for determining the boundaries of a Hall-Wellner band (which is # symmetric). kap.mei <- matrix[,2] sigma <- matrix[,3] result1 <- k*(1+n*sigma)*kap.mei/sqrt(n) result2 <- exp(k*(1+n*sigma)/(sqrt(n)*log(kap.mei))) return(list(lin.dev=result1,log.dev=result2)) } km.ci/R/globals.R0000644000176200001440000000037514222643636013237 0ustar liggesusers#' @importFrom utils globalVariables globalVariables(c("critical.value.hall.90", "critical.value.hall.95", "critical.value.hall.99", "critical.value.nair.90", "critical.value.nair.95", "critical.value.nair.99")) km.ci/R/grunk.all.fun.R0000755000176200001440000000147113351150552014271 0ustar liggesusers"grunk.all.fun" <- function(survi,alpha=0.05) { survi <- survi n.event<- survi$n.event n.lost <- survi$n.risk-c(survi$n.risk[-1],0) n.cens <- n.lost - n.event time <- rep(survi$time,n.lost) len <- length(survi$time) upper <- numeric(len) lower <- numeric(len) status <- numeric() for(i in 1:length(n.cens)) { status <- c(status, rep(0,n.cens[i]),rep(1,n.event[i])) } for (i in 1:len) { if(survi$n.event[i]!=survi$n.risk[i]) { grunk.estimate <- lrt.confints(time,status,survi$time[i],alpha) upper[i] <-grunk.estimate$upper lower[i] <-grunk.estimate$lower } if(survi$n.event[i]==survi$n.risk[i]) { upper[i] <-NA lower[i] <-NA } } survi$upper <- upper survi$lower <- lower return(survi) } km.ci/R/critical.value.R0000644000176200001440000032764614223000620014513 0ustar liggesusers #' @export critical.value.hall.90 <- structure(c(0.59850000000000003, 0.65090000000000003, 0.69789999999999996, 0.74060000000000004, 0.77959999999999996, 0.8155, 0.84870000000000001, 0.87949999999999995, 0.90810000000000002, 0.93479999999999996, 0.9597, 0.9829, 1.0046999999999999, 1.0249999999999999, 1.0439000000000001, 1.0616000000000001, 1.0782, 1.0934999999999999, 1.1077999999999999, 1.1211, 1.1334, 1.1447000000000001, 1.1552, 1.1647000000000001, 1.1734, 1.1813, 1.1883999999999999, 1.1947000000000001, 1.2002999999999999, 1.2052, 1.2094, 1.2130000000000001, 1.2159, 1.2182999999999999, 1.2202, 1.2216, 1.2225999999999999, 1.2232000000000001, 1.2236, 1.2238, 1.2239, 1.2239, 1.2239, 1.2239, 1.2239, 1.2239, 0.59850000000000003, 0.65090000000000003, 0.69789999999999996, 0.74060000000000004, 0.77959999999999996, 0.8155, 0.84870000000000001, 0.87939999999999996, 0.90810000000000002, 0.93479999999999996, 0.9597, 0.9829, 1.0046999999999999, 1.0249999999999999, 1.0439000000000001, 1.0616000000000001, 1.0782, 1.0934999999999999, 1.1077999999999999, 1.1211, 1.1334, 1.1447000000000001, 1.1552, 1.1647000000000001, 1.1734, 1.1813, 1.1883999999999999, 1.1947000000000001, 1.2002999999999999, 1.2052, 1.2094, 1.2129000000000001, 1.2159, 1.2182999999999999, 1.2202, 1.2216, 1.2225999999999999, 1.2232000000000001, 1.2236, 1.2238, 1.2238, 1.2238, 1.2238, 1.2238, 1.2238, 1.2239, 0.59789999999999999, 0.65069999999999995, 0.69779999999999998, 0.74050000000000005, 0.77959999999999996, 0.8155, 0.84870000000000001, 0.87939999999999996, 0.90810000000000002, 0.93479999999999996, 0.9597, 0.9829, 1.0046999999999999, 1.0249999999999999, 1.0439000000000001, 1.0616000000000001, 1.0782, 1.0934999999999999, 1.1077999999999999, 1.1211, 1.1334, 1.1447000000000001, 1.1552, 1.1647000000000001, 1.1734, 1.1813, 1.1883999999999999, 1.1947000000000001, 1.2002999999999999, 1.2052, 1.2094, 1.2129000000000001, 1.2159, 1.2182999999999999, 1.2202, 1.2216, 1.2225999999999999, 1.2232000000000001, 1.2236, 1.2238, 1.2238, 1.2238, 1.2238, 1.2238, 1.2238, 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1.2232000000000001, 1.2232000000000001, 1.2232000000000001, 1.2232000000000001, NA, NA, NA, NA, NA, 0.75249999999999995, 0.80630000000000002, 0.84860000000000002, 0.88470000000000004, 0.91649999999999998, 0.94499999999999995, 0.97099999999999997, 0.99460000000000004, 1.0166999999999999, 1.0369999999999999, 1.0557000000000001, 1.073, 1.089, 1.1039000000000001, 1.1175999999999999, 1.1303000000000001, 1.1418999999999999, 1.1526000000000001, 1.1623000000000001, 1.1712, 1.1793, 1.1865000000000001, 1.1929000000000001, 1.1986000000000001, 1.2036, 1.2078, 1.2115, 1.2144999999999999, 1.2169000000000001, 1.2188000000000001, 1.2202, 1.2212000000000001, 1.2219, 1.2222999999999999, 1.2224999999999999, 1.2224999999999999, 1.2225999999999999, 1.2225999999999999, 1.2225999999999999, 1.2225999999999999, 1.2225999999999999, NA, NA, NA, NA, NA, NA, 0.77729999999999999, 0.82989999999999997, 0.87109999999999999, 0.90600000000000003, 0.93659999999999999, 0.96409999999999996, 0.98899999999999999, 1.0118, 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NA, NA, NA, NA, NA, NA, NA, 0.89239999999999997, 0.93889999999999996, 0.97389999999999999, 1.0026999999999999, 1.0274000000000001, 1.0489999999999999, 1.0682, 1.0852999999999999, 1.1006, 1.1143000000000001, 1.1267, 1.1377999999999999, 1.1476999999999999, 1.1566000000000001, 1.1644000000000001, 1.1713, 1.1773, 1.1823999999999999, 1.1868000000000001, 1.1903999999999999, 1.1933, 1.1956, 1.1974, 1.1986000000000001, 1.1994, 1.1999, 1.2000999999999999, 1.2001999999999999, 1.2002999999999999, 1.2002999999999999, 1.2002999999999999, 1.2002999999999999, 1.2002999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.90200000000000002, 0.94779999999999998, 0.98209999999999997, 1.0102, 1.0342, 1.0550999999999999, 1.0734999999999999, 1.0899000000000001, 1.1046, 1.1176999999999999, 1.1293, 1.1397999999999999, 1.149, 1.1572, 1.1644000000000001, 1.1707000000000001, 1.1759999999999999, 1.1806000000000001, 1.1842999999999999, 1.1874, 1.1898, 1.1916, 1.1929000000000001, 1.1938, 1.1942999999999999, 1.1944999999999999, 1.1946000000000001, 1.1947000000000001, 1.1947000000000001, 1.1947000000000001, 1.1947000000000001, 1.1947000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.91020000000000001, 0.95520000000000005, 0.98880000000000001, 1.0163, 1.0396000000000001, 1.0598000000000001, 1.0774999999999999, 1.0932999999999999, 1.1072, 1.1195999999999999, 1.1307, 1.1404000000000001, 1.149, 1.1566000000000001, 1.1631, 1.1688000000000001, 1.1735, 1.1775, 1.1807000000000001, 1.1832, 1.1851, 1.1865000000000001, 1.1874, 1.1879, 1.1881999999999999, 1.1882999999999999, 1.1882999999999999, 1.1883999999999999, 1.1883999999999999, 1.1883999999999999, 1.1883999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.91690000000000005, 0.96130000000000004, 0.99419999999999997, 1.0209999999999999, 1.0436000000000001, 1.0630999999999999, 1.0802, 1.0952, 1.1085, 1.1203000000000001, 1.1307, 1.1397999999999999, 1.1476999999999999, 1.1546000000000001, 1.1606000000000001, 1.1656, 1.1697, 1.1731, 1.1758, 1.1778, 1.1793, 1.1801999999999999, 1.1808000000000001, 1.1811, 1.1812, 1.1813, 1.1813, 1.1813, 1.1813, 1.1813, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.92230000000000001, 0.96599999999999997, 0.99819999999999998, 1.0243, 1.0462, 1.0650999999999999, 1.0814999999999999, 1.0959000000000001, 1.1085, 1.1195999999999999, 1.1293, 1.1377999999999999, 1.1451, 1.1514, 1.1567000000000001, 1.1611, 1.1647000000000001, 1.1675, 1.1697, 1.1712, 1.1722999999999999, 1.1729000000000001, 1.1732, 1.1733, 1.1734, 1.1734, 1.1734, 1.1734, 1.1734, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.92630000000000001, 0.96930000000000005, 1.0008999999999999, 1.0263, 1.0476000000000001, 1.0658000000000001, 1.0814999999999999, 1.0952, 1.1072, 1.1176999999999999, 1.1267, 1.1345000000000001, 1.1412, 1.1469, 1.1516, 1.1554, 1.1584000000000001, 1.1607000000000001, 1.1623000000000001, 1.1635, 1.1640999999999999, 1.1645000000000001, 1.1646000000000001, 1.1647000000000001, 1.1647000000000001, 1.1647000000000001, 1.1647000000000001, 1.1647000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.92889999999999995, 0.97130000000000005, 1.0022, 1.0269999999999999, 1.0476000000000001, 1.0650999999999999, 1.0802, 1.0932999999999999, 1.1046, 1.1143000000000001, 1.1228, 1.1298999999999999, 1.1359999999999999, 1.141, 1.1451, 1.1483000000000001, 1.1508, 1.1526000000000001, 1.1537999999999999, 1.1545000000000001, 1.1549, 1.1551, 1.1551, 1.1552, 1.1552, 1.1552, 1.1552, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.93020000000000003, 0.97199999999999998, 1.0022, 1.0263, 1.0462, 1.0630999999999999, 1.0774999999999999, 1.0899000000000001, 1.1006, 1.1096999999999999, 1.1174999999999999, 1.1240000000000001, 1.1294, 1.1337999999999999, 1.1373, 1.1399999999999999, 1.1418999999999999, 1.1432, 1.1439999999999999, 1.1445000000000001, 1.1447000000000001, 1.1447000000000001, 1.1447000000000001, 1.1447000000000001, 1.1447000000000001, 1.1447000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.93020000000000003, 0.97130000000000005, 1.0008999999999999, 1.0243, 1.0436000000000001, 1.0598000000000001, 1.0734999999999999, 1.0852999999999999, 1.0952, 1.1036999999999999, 1.1108, 1.1167, 1.1214, 1.1252, 1.1281000000000001, 1.1303000000000001, 1.1316999999999999, 1.1326000000000001, 1.1331, 1.1333, 1.1334, 1.1334, 1.1334, 1.1334, 1.1334, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.92889999999999995, 0.96930000000000005, 0.99819999999999998, 1.0209999999999999, 1.0396000000000001, 1.0550999999999999, 1.0682, 1.0791999999999999, 1.0885, 1.0963000000000001, 1.1027, 1.1079000000000001, 1.1121000000000001, 1.1153, 1.1175999999999999, 1.1192, 1.1202000000000001, 1.1208, 1.121, 1.1211, 1.1211, 1.1211, 1.1211, 1.1211, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.92630000000000001, 0.96599999999999997, 0.99419999999999997, 1.0163, 1.0342, 1.0489999999999999, 1.0613999999999999, 1.0717000000000001, 1.0804, 1.0874999999999999, 1.0931999999999999, 1.0978000000000001, 1.1012999999999999, 1.1039000000000001, 1.1056999999999999, 1.1068, 1.1073999999999999, 1.1076999999999999, 1.1077999999999999, 1.1077999999999999, 1.1077999999999999, 1.1077999999999999, 1.1077999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.92230000000000001, 0.96130000000000004, 0.98880000000000001, 1.0102, 1.0274000000000001, 1.0415000000000001, 1.0531999999999999, 1.0629, 1.0708, 1.0771999999999999, 1.0822000000000001, 1.0862000000000001, 1.089, 1.0911, 1.0923, 1.0931, 1.0933999999999999, 1.0934999999999999, 1.0934999999999999, 1.0934999999999999, 1.0934999999999999, 1.0934999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.91690000000000005, 0.95520000000000005, 0.98209999999999997, 1.0026999999999999, 1.0192000000000001, 1.0326, 1.0436000000000001, 1.0525, 1.0597000000000001, 1.0653999999999999, 1.0697000000000001, 1.073, 1.0752999999999999, 1.0768, 1.0775999999999999, 1.0780000000000001, 1.0781000000000001, 1.0782, 1.0782, 1.0782, 1.0782, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.91020000000000001, 0.94779999999999998, 0.97389999999999999, 0.99380000000000002, 1.0095000000000001, 1.0222, 1.0324, 1.0406, 1.0469999999999999, 1.052, 1.0557000000000001, 1.0583, 1.0600000000000001, 1.0609999999999999, 1.0613999999999999, 1.0616000000000001, 1.0616000000000001, 1.0616000000000001, 1.0616000000000001, 1.0616000000000001), .Dim = c(46L, 31L), .Dimnames = list(c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46"), c("al00", "al02", "al04", "al06", "al08", "al10", "al12", "al14", "al16", "al18", "al20", "al22", "al24", "al26", "al28", "al30", "al32", "al34", "al36", "al38", "al40", "al42", "al44", "al46", "al48", "al50", "al52", "al54", "al56", "al58", "al60"))) #' @export critical.value.hall.95 <- structure(c(0.6825, 0.74180000000000001, 0.79480000000000006, 0.84280000000000022, 0.88660000000000005, 0.92689999999999995, 0.96389999999999998, 0.99819999999999998, 1.0299, 1.0593999999999999, 1.0868, 1.1122999999999998, 1.1359999999999999, 1.1580999999999999, 1.1785000000000001, 1.1976, 1.2151999999999998, 1.2315, 1.2464999999999999, 1.2604, 1.2730999999999999, 1.2847, 1.2952999999999999, 1.3048, 1.3133999999999999, 1.3210999999999999, 1.3279000000000001, 1.3338000000000001, 1.339, 1.3433999999999999, 1.3471, 1.3501000000000001, 1.3525, 1.3544, 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1.0706, 1.0993999999999999, 1.1255999999999999, 1.1495, 1.1714, 1.1915, 1.21, 1.2270000000000001, 1.2425999999999999, 1.2569999999999999, 1.27, 1.282, 1.2927999999999999, 1.3025, 1.3112999999999999, 1.3190999999999999, 1.3261000000000001, 1.3321000000000001, 1.3373999999999999, 1.3418000000000001, 1.3455999999999999, 1.3487, 1.3511, 1.353, 1.3544, 1.3553999999999999, 1.3561000000000001, 1.3565, 1.3567, 1.3567, 1.3568, 1.3568, 1.3568, 1.3568, 1.3568, 1.3568, NA, NA, NA, NA, NA, NA, NA, 0.93149999999999999, 0.98440000000000005, 1.0258, 1.0609999999999999, 1.0918000000000001, 1.1194, 1.1444000000000001, 1.1671, 1.1878, 1.2068000000000001, 1.2242, 1.2401, 1.2546999999999999, 1.268, 1.2801, 1.2910999999999999, 1.3009999999999999, 1.3099000000000001, 1.3178000000000001, 1.3248, 1.3309, 1.3362000000000001, 1.3407, 1.3445, 1.3475999999999999, 1.3501000000000001, 1.3520000000000001, 1.3533999999999999, 1.3544, 1.3551, 1.3554999999999999, 1.3556999999999999, 1.3557999999999999, 1.3557999999999999, 1.3557999999999999, 1.3557999999999999, 1.3557999999999999, 1.3557999999999999, 1.3557999999999999, NA, NA, NA, NA, NA, NA, NA, NA, 0.95540000000000003, 1.0071000000000001, 1.0472999999999999, 1.0812999999999999, 1.1109, 1.1374, 1.1612, 1.1827000000000001, 1.2023999999999999, 1.2202999999999999, 1.2366999999999999, 1.2516, 1.2652000000000001, 1.2775000000000001, 1.2887, 1.2988, 1.3078000000000001, 1.3158000000000001, 1.3229, 1.3290999999999999, 1.3345, 1.3391, 1.3429, 1.3461000000000001, 1.3486, 1.3506, 1.3520000000000001, 1.353, 1.3536999999999999, 1.3541000000000001, 1.3543000000000001, 1.3544, 1.3544, 1.3544, 1.3544, 1.3544, 1.3544, 1.3544, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.97689999999999999, 1.0275000000000001, 1.0666, 1.0993999999999999, 1.1279999999999999, 1.1533, 1.1759999999999999, 1.1966000000000001, 1.2152000000000001, 1.2321, 1.2475000000000001, 1.2615000000000001, 1.2741, 1.2856000000000001, 1.2959000000000001, 1.3050999999999999, 1.3132999999999999, 1.3205, 1.3268, 1.3323, 1.3369, 1.3408, 1.3441000000000001, 1.3466, 1.3486, 1.3501000000000001, 1.3511, 1.3517999999999999, 1.3522000000000001, 1.3524, 1.3525, 1.3525, 1.3525, 1.3525, 1.3525, 1.3525, 1.3525, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 0.99619999999999997, 1.0457000000000001, 1.0838000000000001, 1.1154999999999999, 1.143, 1.1673, 1.1891, 1.2085999999999999, 1.2262999999999999, 1.2422, 1.2566999999999999, 1.2698, 1.2815000000000001, 1.2921, 1.3016000000000001, 1.3100000000000001, 1.3173999999999999, 1.3238000000000001, 1.3293999999999999, 1.3342000000000001, 1.3382000000000001, 1.3413999999999999, 1.3441000000000001, 1.3461000000000001, 1.3475999999999999, 1.3487, 1.3493999999999999, 1.3498000000000001, 1.3500000000000001, 1.3501000000000001, 1.3501000000000001, 1.3501000000000001, 1.3501000000000001, 1.3501000000000001, 1.3501000000000001, 1.3501000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0134000000000001, 1.0619000000000001, 1.0989, 1.1296999999999999, 1.1561999999999999, 1.1796, 1.2002999999999999, 1.2189000000000001, 1.2357, 1.2507999999999999, 1.2643, 1.2765, 1.2874000000000001, 1.2971999999999999, 1.3058000000000001, 1.3133999999999999, 1.3201000000000001, 1.3258000000000001, 1.3307, 1.3348, 1.3382000000000001, 1.3408, 1.3429, 1.3445, 1.3455999999999999, 1.3463000000000001, 1.3467, 1.3469, 1.347, 1.3471, 1.3471, 1.3471, 1.3471, 1.3471, 1.3471, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0286, 1.0761000000000001, 1.1122000000000001, 1.1419999999999999, 1.1676, 1.1899999999999999, 1.2099, 1.2276, 1.2435, 1.2577, 1.2704, 1.2817000000000001, 1.2919, 1.3008, 1.3087, 1.3154999999999999, 1.3214999999999999, 1.3265, 1.3307, 1.3342000000000001, 1.3369, 1.3391, 1.3407, 1.3418000000000001, 1.3426, 1.343, 1.3431999999999999, 1.3432999999999999, 1.3433999999999999, 1.3433999999999999, 1.3433999999999999, 1.3433999999999999, 1.3433999999999999, 1.3433999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0419, 1.0885, 1.1236999999999999, 1.1526000000000001, 1.1773, 1.1988000000000001, 1.2178, 1.2346999999999999, 1.2497, 1.2629999999999999, 1.2748999999999999, 1.2855000000000001, 1.2948, 1.3029999999999999, 1.3101, 1.3162, 1.3214999999999999, 1.3258000000000001, 1.3293999999999999, 1.3323, 1.3345, 1.3362000000000001, 1.3373999999999999, 1.3381000000000001, 1.3386, 1.3388, 1.3389, 1.339, 1.339, 1.339, 1.339, 1.339, 1.339, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0532999999999999, 1.0991, 1.1334, 1.1615, 1.1853, 1.206, 1.2241, 1.2401, 1.2543, 1.2667999999999999, 1.2779, 1.2877000000000001, 1.2963, 1.3037000000000001, 1.3101, 1.3154999999999999, 1.3201000000000001, 1.3238000000000001, 1.3268, 1.3290999999999999, 1.3309, 1.3321000000000001, 1.3329, 1.3333999999999999, 1.3337000000000001, 1.3338000000000001, 1.3338000000000001, 1.3338000000000001, 1.3338000000000001, 1.3338000000000001, 1.3338000000000001, 1.3338000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0630999999999999, 1.1080000000000001, 1.1414, 1.1686000000000001, 1.1916, 1.2115, 1.2287999999999999, 1.244, 1.2574000000000001, 1.2690999999999999, 1.2794000000000001, 1.2884, 1.2963, 1.3029999999999999, 1.3087, 1.3133999999999999, 1.3173999999999999, 1.3205, 1.3229, 1.3248, 1.3261000000000001, 1.3269, 1.3273999999999999, 1.3277000000000001, 1.3278000000000001, 1.3279000000000001, 1.3279000000000001, 1.3279000000000001, 1.3279000000000001, 1.3279000000000001, 1.3279000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0710999999999999, 1.1152, 1.1477999999999999, 1.1741999999999999, 1.1963999999999999, 1.2154, 1.2319, 1.2463, 1.2588999999999999, 1.2699, 1.2794000000000001, 1.2877000000000001, 1.2948, 1.3008, 1.3058000000000001, 1.3100000000000001, 1.3132999999999999, 1.3158000000000001, 1.3178000000000001, 1.3190999999999999, 1.3201000000000001, 1.3206, 1.3209, 1.321, 1.3210999999999999, 1.3210999999999999, 1.3210999999999999, 1.3210999999999999, 1.3210999999999999, 1.3210999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0774999999999999, 1.1208, 1.1526000000000001, 1.1780999999999999, 1.1995, 1.2177, 1.2335, 1.2471000000000001, 1.2588999999999999, 1.2690999999999999, 1.2779, 1.2855000000000001, 1.2919, 1.2971999999999999, 1.3016000000000001, 1.3050999999999999, 1.3078000000000001, 1.3099000000000001, 1.3112999999999999, 1.3123, 1.3129, 1.3131999999999999, 1.3132999999999999, 1.3133999999999999, 1.3133999999999999, 1.3133999999999999, 1.3133999999999999, 1.3133999999999999, 1.3133999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0822000000000001, 1.1247, 1.1556999999999999, 1.1805000000000001, 1.2011000000000001, 1.2184999999999999, 1.2335, 1.2463, 1.2574000000000001, 1.2667999999999999, 1.2748999999999999, 1.2817000000000001, 1.2874000000000001, 1.2921, 1.2959000000000001, 1.2988, 1.3009999999999999, 1.3025, 1.3036000000000001, 1.3042, 1.3046, 1.3047, 1.3048, 1.3048, 1.3048, 1.3048, 1.3048, 1.3048, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0853999999999999, 1.1271, 1.1573, 1.1813, 1.2011000000000001, 1.2177, 1.2319, 1.244, 1.2543, 1.2629999999999999, 1.2704, 1.2765, 1.2815000000000001, 1.2856000000000001, 1.2887, 1.2910999999999999, 1.2927999999999999, 1.2939000000000001, 1.2946, 1.2949999999999999, 1.2951999999999999, 1.2951999999999999, 1.2951999999999999, 1.2951999999999999, 1.2951999999999999, 1.2951999999999999, 1.2951999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0869, 1.1278999999999999, 1.1573, 1.1805000000000001, 1.1995, 1.2154, 1.2287999999999999, 1.2401, 1.2497, 1.2577, 1.2643, 1.2698, 1.2741, 1.2775000000000001, 1.2801, 1.282, 1.2831999999999999, 1.284, 1.2844, 1.2846, 1.2847, 1.2847, 1.2847, 1.2847, 1.2847, 1.2847, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0869, 1.1271, 1.1556999999999999, 1.1780999999999999, 1.1963999999999999, 1.2115, 1.2241, 1.2346999999999999, 1.2435, 1.2507999999999999, 1.2566999999999999, 1.2615000000000001, 1.2652000000000001, 1.268, 1.27, 1.2714000000000001, 1.2723, 1.2727999999999999, 1.2729999999999999, 1.2730999999999999, 1.2730999999999999, 1.2730999999999999, 1.2730999999999999, 1.2730999999999999, 1.2730999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0853999999999999, 1.1247, 1.1526000000000001, 1.1741999999999999, 1.1916, 1.206, 1.2178, 1.2276, 1.2357, 1.2422, 1.2475000000000001, 1.2516, 1.2546999999999999, 1.2569999999999999, 1.2585, 1.2595000000000001, 1.26, 1.2603, 1.2603, 1.2604, 1.2604, 1.2604, 1.2604, 1.2604, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0822000000000001, 1.1208, 1.1477999999999999, 1.1686000000000001, 1.1853, 1.1988000000000001, 1.2099, 1.2189000000000001, 1.2262999999999999, 1.2321, 1.2366999999999999, 1.2401, 1.2425999999999999, 1.2444, 1.2455000000000001, 1.2461, 1.2464, 1.2464999999999999, 1.2464999999999999, 1.2464999999999999, 1.2464999999999999, 1.2464999999999999, 1.2464999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0774999999999999, 1.1152, 1.1414, 1.1615, 1.1773, 1.1899999999999999, 1.2002999999999999, 1.2085999999999999, 1.2152000000000001, 1.2202999999999999, 1.2242, 1.2270000000000001, 1.2290000000000001, 1.2302, 1.2310000000000001, 1.2313000000000001, 1.2314000000000001, 1.2315, 1.2315, 1.2315, 1.2315, 1.2315, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0710999999999999, 1.1080000000000001, 1.1334, 1.1526000000000001, 1.1676, 1.1796, 1.1891, 1.1966000000000001, 1.2023999999999999, 1.2068000000000001, 1.21, 1.2122999999999999, 1.2137, 1.2145999999999999, 1.2150000000000001, 1.2151000000000001, 1.2152000000000001, 1.2152000000000001, 1.2152000000000001, 1.2152000000000001, 1.2152000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.0630999999999999, 1.0991, 1.1236999999999999, 1.1419999999999999, 1.1561999999999999, 1.1673, 1.1759999999999999, 1.1827000000000001, 1.1878, 1.1915, 1.1940999999999999, 1.1958, 1.1968000000000001, 1.1973, 1.1975, 1.1975, 1.1976, 1.1976, 1.1976, 1.1976), .Dim = c(46L, 31L), .Dimnames = list( c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46"), c("al00", "al02", "al04", "al06", "al08", "al10", "al12", "al14", "al16", "al18", "al20", "al22", "al24", "al26", "al28", "al30", "al32", "al34", "al36", "al38", "al40", "al42", "al44", "al46", "al48", "al50", "al52", "al54", "al56", "al58", "al60"))) #' @export critical.value.hall.99 <- structure(c(0.85119999999999996, 0.92430000000000001, 0.98950000000000005, 1.0483, 1.1016999999999999, 1.1505000000000001, 1.1953, 1.2364999999999999, 1.2745, 1.3095000000000001, 1.3419000000000001, 1.3716999999999999, 1.3993, 1.4247000000000001, 1.4480999999999999, 1.4696, 1.4893000000000001, 1.5073000000000001, 1.5237000000000001, 1.5386, 1.552, 1.5640000000000001, 1.5747, 1.5841000000000001, 1.5924, 1.5995999999999999, 1.6056999999999999, 1.6109, 1.6152, 1.6186, 1.6214, 1.6234999999999999, 1.625, 1.6261000000000001, 1.6268, 1.6272, 1.6274999999999999, 1.6275999999999999, 1.6275999999999999, 1.6275999999999999, 1.6275999999999999, 1.6275999999999999, 1.6275999999999999, 1.6275999999999999, 1.6275999999999999, 1.6275999999999999, 0.85119999999999996, 0.92430000000000001, 0.98950000000000005, 1.0483, 1.1016999999999999, 1.1505000000000001, 1.1953, 1.2364999999999999, 1.2745, 1.3095000000000001, 1.3419000000000001, 1.3716999999999999, 1.3993, 1.4247000000000001, 1.4480999999999999, 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1.5166999999999999, 1.6194, 1.5213000000000001, 1.5225, 1.5230999999999999, 1.5235000000000001, 1.5236000000000001, 1.5237000000000001, 1.5237000000000001, 1.5237000000000001, 1.5237000000000001, 1.5237000000000001, 1.5237000000000001, 1.5237000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.3808, 1.4160999999999999, 1.4399, 1.4574, 1.4706999999999999, 1.4810000000000001, 1.4887999999999999, 1.4947999999999999, 1.4992000000000001, 1.5023, 1.5044999999999999, 1.5058, 1.5065999999999999, 1.5071000000000001, 1.5072000000000001, 1.5073000000000001, 1.5073000000000001, 1.5073000000000001, 1.5073000000000001, 1.5073000000000001, 1.5073000000000001, 1.5073000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.3724000000000001, 1.4067000000000001, 1.4294, 1.4459, 1.4582999999999999, 1.4676, 1.4745999999999999, 1.4797, 1.4834000000000001, 1.4859, 1.4875, 1.4884999999999999, 1.4890000000000001, 1.4892000000000001, 1.4893000000000001, 1.4893000000000001, 1.4893000000000001, 1.4893000000000001, 1.4893000000000001, 1.4893000000000001, 1.4893000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 1.3619000000000001, 1.395, 1.4167000000000001, 1.4321999999999999, 1.4436, 1.452, 1.4581999999999999, 1.4624999999999999, 1.4655, 1.4674, 1.4685999999999999, 1.4692000000000001, 1.4695, 1.4696, 1.4696, 1.4696, 1.4696, 1.4696, 1.4696, 1.4696), .Dim = c(46L, 31L), .Dimnames = list(c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45", "46" ), c("al00", "al02", "al04", "al06", "al08", "al10", "al12", "al14", "al16", "al18", "al20", "al22", "al24", "al26", "al28", "al30", "al32", "al34", "al36", "al38", "al40", "al42", "al44", "al46", "al48", "al50", "al52", "al54", "al56", "al58", "al60" ))) #' @export critical.value.nair.90 <- structure(c(2.4546999999999999, 2.4906999999999999, 2.5198, 2.5440999999999998, 2.5649999999999999, 2.5832999999999999, 2.5996999999999999, 2.6143999999999998, 2.6278000000000001, 2.6402000000000001, 2.6516999999999999, 2.6625000000000001, 2.6726999999999999, 2.6823000000000001, 2.6915, 2.7002999999999999, 2.7088000000000001, 2.7170000000000001, 2.7248999999999999, 2.7326000000000001, 2.7402000000000002, 2.7475999999999998, 2.7547999999999999, 2.762, 2.7690999999999999, 2.7761999999999998, 2.7833000000000001, 2.7904, 2.7974999999999999, 2.8046000000000002, 2.8119000000000001, 2.8193000000000001, 2.8269000000000002, 2.8347000000000002, 2.8428, 2.8512, 2.8601000000000001, 2.8694999999999999, 2.8797000000000001, 2.8908, 2.9032, 2.9176000000000002, 2.9348000000000001, 2.9573, 2.9918999999999998, 2.3048999999999999, 2.3521000000000001, 2.3900999999999999, 2.4217, 2.4485999999999999, 2.4721000000000002, 2.4929000000000001, 2.5116000000000001, 2.5286, 2.5440999999999998, 2.5586000000000002, 2.5720000000000001, 2.5846, 2.5964999999999998, 2.6078000000000001, 2.6185999999999998, 2.629, 2.6389999999999998, 2.6486000000000001, 2.6579000000000002, 2.6671, 2.6760000000000002, 2.6846999999999999, 2.6932999999999998, 2.7018, 2.7103000000000002, 2.7185999999999999, 2.7269999999999999, 2.7353999999999998, 2.7439, 2.7524000000000002, 2.7610999999999999, 2.77, 2.7789999999999999, 2.7884000000000002, 2.7982, 2.8085, 2.8193000000000001, 2.831, 2.8437000000000001, 2.8578999999999999, 2.8740999999999999, 2.8936000000000002, 2.9188000000000001, 2.9573, 2.1947000000000001, 2.2496999999999998, 2.2942, 2.3313000000000001, 2.363, 2.3906000000000001, 2.415, 2.4367999999999999, 2.4567000000000001, 2.4748000000000001, 2.4914999999999998, 2.5070999999999999, 2.5217000000000001, 2.5354000000000001, 2.5484, 2.5608, 2.5726, 2.5840000000000001, 2.5950000000000002, 2.6055999999999999, 2.6160000000000001, 2.6261000000000001, 2.6358999999999999, 2.6456, 2.6551999999999998, 2.6646999999999998, 2.6741000000000001, 2.6835, 2.6928999999999998, 2.7023000000000001, 2.7118000000000002, 2.7214, 2.7313000000000001, 2.7412999999999998, 2.7517, 2.7624, 2.7736999999999998, 2.7856000000000001, 2.7984, 2.8123, 2.8277000000000001, 2.8454000000000002, 2.8664000000000001, 2.8936000000000002, 2.9348000000000001, 2.1053999999999999, 2.1654, 2.2147000000000001, 2.2561, 2.2917000000000001, 2.3227000000000002, 2.3500999999999999, 2.3746999999999998, 2.3969999999999998, 2.4174000000000002, 2.4361000000000002, 2.4535999999999998, 2.4698000000000002, 2.4851999999999999, 2.4996999999999998, 2.5133999999999999, 2.5266000000000002, 2.5392000000000001, 2.5514000000000001, 2.5630999999999999, 2.5745, 2.5857000000000001, 2.5964999999999998, 2.6072000000000002, 2.6177000000000001, 2.6280999999999999, 2.6383999999999999, 2.6486000000000001, 2.6587999999999998, 2.6690999999999998, 2.6793999999999998, 2.6899000000000002, 2.7004999999999999, 2.7113999999999998, 2.7225999999999999, 2.7342, 2.7463000000000002, 2.7591999999999999, 2.7728000000000002, 2.7877000000000001, 2.8041999999999998, 2.823, 2.8454000000000002, 2.8740999999999999, 2.9176000000000002, NA, 2.0933000000000002, 2.1457999999999999, 2.1905000000000001, 2.2290999999999999, 2.2629999999999999, 2.2930000000000001, 2.3199999999999998, 2.3445, 2.3668, 2.3874, 2.4064999999999999, 2.4243999999999999, 2.4411999999999998, 2.4569999999999999, 2.4721000000000002, 2.4864999999999999, 2.5002, 2.5133999999999999, 2.5261999999999998, 2.5386000000000002, 2.5507, 2.5625, 2.5739999999999998, 2.5853000000000002, 2.5964999999999998, 2.6076000000000001, 2.6185999999999998, 2.6295999999999999, 2.6406999999999998, 2.6516999999999999, 2.6629, 2.6743000000000001, 2.6859000000000002, 2.6979000000000002, 2.7103000000000002, 2.7231999999999998, 2.7366999999999999, 2.7513000000000001, 2.7669999999999999, 2.7844000000000002, 2.8041999999999998, 2.8277000000000001, 2.8578999999999999, 2.9032, NA, NA, 2.0849000000000002, 2.1318000000000001, 2.1728000000000001, 2.2090000000000001, 2.2412000000000001, 2.2703000000000002, 2.2967, 2.3208000000000002, 2.3431000000000002, 2.3637999999999999, 2.3831000000000002, 2.4011999999999998, 2.4182999999999999, 2.4346000000000001, 2.4500999999999999, 2.4649000000000001, 2.4792000000000001, 2.4929000000000001, 2.5062000000000002, 2.5192000000000001, 2.5318000000000001, 2.5440999999999998, 2.5562999999999998, 2.5682, 2.5800999999999998, 2.5918000000000001, 2.6036000000000001, 2.6153, 2.6271, 2.6389999999999998, 2.6509999999999998, 2.6633, 2.6760000000000002, 2.6890000000000001, 2.7025999999999999, 2.7170000000000001, 2.7322000000000002, 2.7486999999999999, 2.7669999999999999, 2.7877000000000001, 2.8123, 2.8437000000000001, 2.8908, NA, NA, NA, 2.0788000000000002, 2.1214, 2.1594000000000002, 2.1934, 2.2242000000000002, 2.2523, 2.2780999999999998, 2.3018999999999998, 2.3239999999999998, 2.3445999999999998, 2.3639999999999999, 2.3824000000000001, 2.3997000000000002, 2.4163000000000001, 2.4321000000000002, 2.4474, 2.4620000000000002, 2.4762, 2.4900000000000002, 2.5034999999999998, 2.5165999999999999, 2.5295000000000001, 2.5421999999999998, 2.5548000000000002, 2.5672000000000001, 2.5796000000000001, 2.5920000000000001, 2.6044999999999998, 2.617, 2.6297000000000001, 2.6427, 2.6560000000000001, 2.6697000000000002, 2.6840000000000002, 2.6989999999999998, 2.7149999999999999, 2.7322000000000002, 2.7513000000000001, 2.7728000000000002, 2.7984, 2.831, 2.8797000000000001, NA, NA, NA, NA, 2.0741999999999998, 2.1133999999999999, 2.1488999999999998, 2.1810999999999998, 2.2107000000000001, 2.2378, 2.2629999999999999, 2.2864, 2.3083, 2.3289, 2.3483999999999998, 2.3668, 2.3843999999999999, 2.4011999999999998, 2.4174000000000002, 2.4329000000000001, 2.448, 2.4626000000000001, 2.4767999999999999, 2.4906999999999999, 2.5043000000000002, 2.5177999999999998, 2.5310000000000001, 2.5440999999999998, 2.5571999999999999, 2.5703, 2.5832999999999999, 2.5964999999999998, 2.6099000000000001, 2.6234999999999999, 2.6374, 2.6516999999999999, 2.6667000000000001, 2.6823000000000001, 2.6989999999999998, 2.7170000000000001, 2.7366999999999999, 2.7591999999999999, 2.7856000000000001, 2.8193000000000001, 2.8694999999999999, NA, NA, NA, NA, NA, 2.0706000000000002, 2.1071, 2.1404999999999998, 2.1711999999999998, 2.1996000000000002, 2.226, 2.2505999999999999, 2.2736000000000001, 2.2953000000000001, 2.3159000000000001, 2.3353000000000002, 2.3538999999999999, 2.3715999999999999, 2.3887, 2.4051, 2.4209999999999998, 2.4363999999999999, 2.4514, 2.4660000000000002, 2.4803999999999999, 2.4944999999999999, 2.5084, 2.5222000000000002, 2.5358999999999998, 2.5495999999999999, 2.5632999999999999, 2.5771000000000002, 2.5911, 2.6053000000000002, 2.6198000000000001, 2.6347999999999998, 2.6503999999999999, 2.6667000000000001, 2.6840000000000002, 2.7025999999999999, 2.7231999999999998, 2.7463000000000002, 2.7736999999999998, 2.8085, 2.8601000000000001, NA, NA, NA, NA, NA, NA, 2.0676999999999999, 2.1019000000000001, 2.1335999999999999, 2.1631, 2.1905000000000001, 2.2162000000000002, 2.2403, 2.2629999999999999, 2.2845, 2.3048999999999999, 2.3243999999999998, 2.3431000000000002, 2.3610000000000002, 2.3782000000000001, 2.3948999999999998, 2.4110999999999998, 2.4268999999999998, 2.4422000000000001, 2.4573, 2.4721000000000002, 2.4866999999999999, 2.5011000000000001, 2.5154999999999998, 2.5297999999999998, 2.5440999999999998, 2.5586000000000002, 2.5731000000000002, 2.5878999999999999, 2.6031, 2.6185999999999998, 2.6347999999999998, 2.6516999999999999, 2.6697000000000002, 2.6890000000000001, 2.7103000000000002, 2.7342, 2.7624, 2.7982, 2.8512, NA, NA, NA, NA, NA, NA, NA, 2.0653999999999999, 2.0977999999999999, 2.1280000000000001, 2.1562999999999999, 2.1829000000000001, 2.2080000000000002, 2.2315999999999998, 2.2541000000000002, 2.2753999999999999, 2.2957999999999998, 2.3153000000000001, 2.3340999999999998, 2.3521000000000001, 2.3696000000000002, 2.3864999999999998, 2.403, 2.4190999999999998, 2.4348999999999998, 2.4502999999999999, 2.4655999999999998, 2.4807000000000001, 2.4956999999999998, 2.5106000000000002, 2.5255999999999998, 2.5406, 2.5558000000000001, 2.5712000000000002, 2.5869, 2.6031, 2.6198000000000001, 2.6374, 2.6560000000000001, 2.6760000000000002, 2.6979000000000002, 2.7225999999999999, 2.7517, 2.7884000000000002, 2.8428, NA, NA, NA, NA, NA, NA, NA, NA, 2.0634000000000001, 2.0943000000000001, 2.1233, 2.1507000000000001, 2.1766000000000001, 2.2010999999999998, 2.2244000000000002, 2.2465999999999999, 2.2677999999999998, 2.2881, 2.3077000000000001, 2.3264999999999998, 2.3448000000000002, 2.3624999999999998, 2.3797000000000001, 2.3965000000000001, 2.4129, 2.4291, 2.4449999999999998, 2.4607000000000001, 2.4763000000000002, 2.4918999999999998, 2.5074999999999998, 2.5230999999999999, 2.5388000000000002, 2.5548000000000002, 2.5712000000000002, 2.5878999999999999, 2.6053000000000002, 2.6234999999999999, 2.6427, 2.6633, 2.6859000000000002, 2.7113999999999998, 2.7412999999999998, 2.7789999999999999, 2.8347000000000002, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0617999999999999, 2.0914000000000001, 2.1194000000000002, 2.1459999999999999, 2.1713, 2.1953, 2.2183000000000002, 2.2403, 2.2614000000000001, 2.2818000000000001, 2.3014000000000001, 2.3203, 2.3388, 2.3567, 2.3742000000000001, 2.3913000000000002, 2.4081000000000001, 2.4247000000000001, 2.4411, 2.4573, 2.4735, 2.4897, 2.5059, 2.5222000000000002, 2.5388000000000002, 2.5558000000000001, 2.5731000000000002, 2.5911, 2.6099000000000001, 2.6297000000000001, 2.6509999999999998, 2.6743000000000001, 2.7004999999999999, 2.7313000000000001, 2.77, 2.8269000000000002, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0605000000000002, 2.089, 2.1162000000000001, 2.1421000000000001, 2.1667999999999998, 2.1905000000000001, 2.2132000000000001, 2.2351000000000001, 2.2561, 2.2765, 2.2961999999999998, 2.3153000000000001, 2.3338999999999999, 2.3521000000000001, 2.3698999999999999, 2.3874, 2.4045999999999998, 2.4217, 2.4384999999999999, 2.4552999999999998, 2.4721000000000002, 2.4889000000000001, 2.5059, 2.5230999999999999, 2.5406, 2.5586000000000002, 2.5771000000000002, 2.5964999999999998, 2.617, 2.6389999999999998, 2.6629, 2.6899000000000002, 2.7214, 2.7610999999999999, 2.8193000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0594000000000001, 2.0870000000000002, 2.1133999999999999, 2.1387, 2.1631, 2.1865000000000001, 2.2090000000000001, 2.2307000000000001, 2.2517999999999998, 2.2722000000000002, 2.2919999999999998, 2.3113000000000001, 2.3302, 2.3487, 2.3668, 2.3847, 2.4022999999999999, 2.4198, 2.4373, 2.4546999999999999, 2.4721000000000002, 2.4897, 2.5074999999999998, 2.5255999999999998, 2.5440999999999998, 2.5632999999999999, 2.5832999999999999, 2.6044999999999998, 2.6271, 2.6516999999999999, 2.6793999999999998, 2.7118000000000002, 2.7524000000000002, 2.8119000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0585, 2.0853000000000002, 2.1111, 2.1360000000000001, 2.1600000000000001, 2.1831, 2.2054999999999998, 2.2271999999999998, 2.2483, 2.2688000000000001, 2.2888000000000002, 2.3083, 2.3275000000000001, 2.3462999999999998, 2.3647999999999998, 2.3831000000000002, 2.4011999999999998, 2.4192, 2.4373, 2.4552999999999998, 2.4735, 2.4918999999999998, 2.5106000000000002, 2.5297999999999998, 2.5495999999999999, 2.5703, 2.5920000000000001, 2.6153, 2.6406999999999998, 2.6690999999999998, 2.7023000000000001, 2.7439, 2.8046000000000002, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0577000000000001, 2.0838999999999999, 2.1092, 2.1337000000000002, 2.1574, 2.1804000000000001, 2.2027000000000001, 2.2244000000000002, 2.2456, 2.2662, 2.2864, 2.3062, 2.3256999999999999, 2.3448000000000002, 2.3637999999999999, 2.3824999999999998, 2.4011999999999998, 2.4198, 2.4384999999999999, 2.4573, 2.4763000000000002, 2.4956999999999998, 2.5154999999999998, 2.5358999999999998, 2.5571999999999999, 2.5796000000000001, 2.6036000000000001, 2.6295999999999999, 2.6587999999999998, 2.6928999999999998, 2.7353999999999998, 2.7974999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0569999999999999, 2.0827, 2.1076000000000001, 2.1318000000000001, 2.1554000000000002, 2.1783000000000001, 2.2006000000000001, 2.2223000000000002, 2.2435999999999998, 2.2644000000000002, 2.2848000000000002, 2.3048999999999999, 2.3248000000000002, 2.3443000000000001, 2.3637999999999999, 2.3831000000000002, 2.4022999999999999, 2.4217, 2.4411, 2.4607000000000001, 2.4807000000000001, 2.5011000000000001, 2.5222000000000002, 2.5440999999999998, 2.5672000000000001, 2.5918000000000001, 2.6185999999999998, 2.6486000000000001, 2.6835, 2.7269999999999999, 2.7904, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0565000000000002, 2.0817999999999999, 2.1063999999999998, 2.1303999999999998, 2.1537999999999999, 2.1766000000000001, 2.1989999999999998, 2.2208000000000001, 2.2423000000000002, 2.2633000000000001, 2.2841, 2.3045, 2.3248000000000002, 2.3448000000000002, 2.3647999999999998, 2.3847, 2.4045999999999998, 2.4247000000000001, 2.4449999999999998, 2.4655999999999998, 2.4866999999999999, 2.5084, 2.5310000000000001, 2.5548000000000002, 2.5800999999999998, 2.6076000000000001, 2.6383999999999999, 2.6741000000000001, 2.7185999999999999, 2.7833000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0560999999999998, 2.081, 2.1053999999999999, 2.1293000000000002, 2.1526000000000001, 2.1755, 2.1979000000000002, 2.2200000000000002, 2.2416, 2.2629999999999999, 2.2841, 2.3048999999999999, 2.3256999999999999, 2.3462999999999998, 2.3668, 2.3874, 2.4081000000000001, 2.4291, 2.4502999999999999, 2.4721000000000002, 2.4944999999999999, 2.5177999999999998, 2.5421999999999998, 2.5682, 2.5964999999999998, 2.6280999999999999, 2.6646999999999998, 2.7103000000000002, 2.7761999999999998, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0556999999999999, 2.0804, 2.1046999999999998, 2.1284999999999998, 2.1518000000000002, 2.1747999999999998, 2.1974, 2.2197, 2.2416, 2.2633000000000001, 2.2848000000000002, 2.3062, 2.3275000000000001, 2.3487, 2.3698999999999999, 2.3913000000000002, 2.4129, 2.4348999999999998, 2.4573, 2.4803999999999999, 2.5043000000000002, 2.5295000000000001, 2.5562999999999998, 2.5853000000000002, 2.6177000000000001, 2.6551999999999998, 2.7018, 2.7690999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0554999999999999, 2.0800000000000001, 2.1042000000000001, 2.1280000000000001, 2.1515, 2.1745999999999999, 2.1974, 2.2200000000000002, 2.2423000000000002, 2.2644000000000002, 2.2864, 2.3083, 2.3302, 2.3521000000000001, 2.3742000000000001, 2.3965000000000001, 2.4190999999999998, 2.4422000000000001, 2.4660000000000002, 2.4906999999999999, 2.5165999999999999, 2.5440999999999998, 2.5739999999999998, 2.6072000000000002, 2.6456, 2.6932999999999998, 2.762, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0552999999999999, 2.0798000000000001, 2.1040000000000001, 2.1278999999999999, 2.1515, 2.1747999999999998, 2.1979000000000002, 2.2208000000000001, 2.2435999999999998, 2.2662, 2.2888000000000002, 2.3113000000000001, 2.3338999999999999, 2.3567, 2.3797000000000001, 2.403, 2.4268999999999998, 2.4514, 2.4767999999999999, 2.5034999999999998, 2.5318000000000001, 2.5625, 2.5964999999999998, 2.6358999999999999, 2.6846999999999999, 2.7547999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0552999999999999, 2.0796999999999999, 2.1040000000000001, 2.1280000000000001, 2.1518000000000002, 2.1755, 2.1989999999999998, 2.2223000000000002, 2.2456, 2.2688000000000001, 2.2919999999999998, 2.3153000000000001, 2.3388, 2.3624999999999998, 2.3864999999999998, 2.4110999999999998, 2.4363999999999999, 2.4626000000000001, 2.4900000000000002, 2.5192000000000001, 2.5507, 2.5857000000000001, 2.6261000000000001, 2.6760000000000002, 2.7475999999999998, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0552999999999999, 2.0798000000000001, 2.1042000000000001, 2.1284999999999998, 2.1526000000000001, 2.1766000000000001, 2.2006000000000001, 2.2244000000000002, 2.2483, 2.2722000000000002, 2.2961999999999998, 2.3203, 2.3448000000000002, 2.3696000000000002, 2.3948999999999998, 2.4209999999999998, 2.448, 2.4762, 2.5062000000000002, 2.5386000000000002, 2.5745, 2.6160000000000001, 2.6671, 2.7402000000000002, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0552999999999999, 2.0800000000000001, 2.1046999999999998, 2.1293000000000002, 2.1537999999999999, 2.1783000000000001, 2.2027000000000001, 2.2271999999999998, 2.2517999999999998, 2.2765, 2.3014000000000001, 2.3264999999999998, 2.3521000000000001, 2.3782000000000001, 2.4051, 2.4329000000000001, 2.4620000000000002, 2.4929000000000001, 2.5261999999999998, 2.5630999999999999, 2.6055999999999999, 2.6579000000000002, 2.7326000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0554999999999999, 2.0804, 2.1053999999999999, 2.1303999999999998, 2.1554000000000002, 2.1804000000000001, 2.2054999999999998, 2.2307000000000001, 2.2561, 2.2818000000000001, 2.3077000000000001, 2.3340999999999998, 2.3610000000000002, 2.3887, 2.4174000000000002, 2.4474, 2.4792000000000001, 2.5133999999999999, 2.5514000000000001, 2.5950000000000002, 2.6486000000000001, 2.7248999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0556999999999999, 2.081, 2.1063999999999998, 2.1318000000000001, 2.1574, 2.1831, 2.2090000000000001, 2.2351000000000001, 2.2614000000000001, 2.2881, 2.3153000000000001, 2.3431000000000002, 2.3715999999999999, 2.4011999999999998, 2.4321000000000002, 2.4649000000000001, 2.5002, 2.5392000000000001, 2.5840000000000001, 2.6389999999999998, 2.7170000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0560999999999998, 2.0817999999999999, 2.1076000000000001, 2.1337000000000002, 2.1600000000000001, 2.1865000000000001, 2.2132000000000001, 2.2403, 2.2677999999999998, 2.2957999999999998, 2.3243999999999998, 2.3538999999999999, 2.3843999999999999, 2.4163000000000001, 2.4500999999999999, 2.4864999999999999, 2.5266000000000002, 2.5726, 2.629, 2.7088000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.0565000000000002, 2.0827, 2.1092, 2.1360000000000001, 2.1631, 2.1905000000000001, 2.2183000000000002, 2.2465999999999999, 2.2753999999999999, 2.3048999999999999, 2.3353000000000002, 2.3668, 2.3997000000000002, 2.4346000000000001, 2.4721000000000002, 2.5133999999999999, 2.5608, 2.6185999999999998, 2.7002999999999999), .Dim = c(45L, 30L), .Dimnames = list( c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45"), c("al02", "al04", "al06", "al08", "al10", "al12", "al14", "al16", "al18", "al20", "al22", "al24", "al26", "al28", "al30", "al32", "al34", "al36", "al38", "al40", "al42", "al44", "al46", "al48", "al50", "al52", "al54", "al56", "al58", "al60"))) #' @export critical.value.nair.95 <- structure(c(2.75, 2.7841, 2.8113999999999999, 2.8341000000000003, 2.8534999999999999, 2.8704000000000001, 2.8855, 2.899, 2.9114, 2.9226999999999999, 2.9333, 2.9432, 2.9524999999999997, 2.9613, 2.9696000000000002, 2.9777, 2.9853999999999998, 2.9927999999999999, 3.0001000000000002, 3.0071000000000003, 3.0140000000000002, 3.0207000000000002, 3.0272999999999999, 3.0338000000000003, 3.0402999999999998, 3.0468000000000002, 3.0531999999999999, 3.0596000000000001, 3.0661, 3.0726, 3.0792000000000002, 3.0859000000000001, 3.0928, 3.0998999999999999, 3.1071999999999997, 3.1149, 3.1230000000000002, 3.1315, 3.1408, 3.1509, 3.1621999999999999, 3.1751999999999998, 3.1909000000000001, 3.2113, 3.2427999999999999, 2.6032999999999999, 2.6505999999999998, 2.6879, 2.7183999999999999, 2.7442000000000002, 2.7665999999999999, 2.7862, 2.8037000000000001, 2.8196000000000003, 2.8341000000000003, 2.8475000000000001, 2.8599000000000001, 2.8715999999999999, 2.8826000000000001, 2.8929999999999998, 2.9028999999999998, 2.9123999999999999, 2.9216000000000002, 2.9303999999999997, 2.9390000000000001, 2.9472999999999998, 2.9554, 2.9634, 2.9713000000000003, 2.9790000000000001, 2.9866999999999999, 2.9943999999999997, 3.0019999999999998, 3.0095999999999998, 3.0172999999999996, 3.0251000000000001, 3.0329999999999999, 3.0411000000000001, 3.0492999999999997, 3.0579000000000001, 3.0667, 3.0760999999999998, 3.0859000000000001, 3.0964999999999998, 3.1080999999999999, 3.1208999999999998, 3.1356999999999999, 3.1534, 3.1763000000000003, 3.2113, 2.4874000000000001, 2.5463, 2.5924, 2.6299000000000001, 2.6614, 2.6884000000000001, 2.7120000000000002, 2.7329999999999997, 2.7519, 2.7690999999999999, 2.7848999999999999, 2.7995000000000001, 2.8130999999999999, 2.8260000000000001, 2.8380999999999998, 2.8494999999999999, 2.8605, 2.871, 2.8812000000000002, 2.891, 2.9005000000000001, 2.9097, 2.9188000000000001, 2.9277000000000002, 2.9364999999999997, 2.9451000000000001, 2.9537, 2.9622999999999999, 2.9708999999999999, 2.9795000000000003, 2.9881000000000002, 2.9969000000000001, 3.0059, 3.0149999999999997, 3.0244, 3.0341999999999998, 3.0445000000000002, 3.0552999999999999, 3.0669, 3.0795000000000003, 3.0934999999999997, 3.1095999999999999, 3.1286999999999998, 3.1534, 3.1909000000000001, 2.3859000000000004, 2.4547999999999996, 2.5089999999999999, 2.5529999999999999, 2.5897999999999999, 2.6213000000000002, 2.6486999999999998, 2.6728999999999998, 2.6946000000000003, 2.7143000000000002, 2.7323, 2.7489999999999997, 2.7643999999999997, 2.7789000000000001, 2.7925, 2.8054999999999999, 2.8178000000000001, 2.8295000000000003, 2.8408000000000002, 2.8517000000000001, 2.8623000000000003, 2.8725999999999998, 2.8826000000000001, 2.8923999999999999, 2.9020999999999999, 2.9116, 2.9210000000000003, 2.9303999999999997, 2.9398, 2.9492000000000003, 2.9585999999999997, 2.9681999999999999, 2.9779, 2.9878, 2.9980000000000002, 3.0085999999999999, 3.0196000000000001, 3.0312000000000001, 3.0437000000000003, 3.0571999999999999, 3.0722, 3.0891999999999999, 3.1095999999999999, 3.1356999999999999, 3.1751999999999998, NA, 2.3715000000000002, 2.4327000000000001, 2.4827000000000004, 2.5245000000000002, 2.5602, 2.5911999999999997, 2.6185999999999998, 2.6429999999999998, 2.6650999999999998, 2.6853000000000002, 2.7039, 2.7210999999999999, 2.7372000000000001, 2.7523, 2.7665999999999999, 2.7801, 2.7930999999999999, 2.8054999999999999, 2.8174000000000001, 2.8289999999999997, 2.8402000000000003, 2.8510999999999997, 2.8617999999999997, 2.8723000000000001, 2.8826000000000001, 2.8928000000000003, 2.9028999999999998, 2.9129999999999998, 2.9231000000000003, 2.9333, 2.9434999999999998, 2.9539, 2.9645999999999999, 2.9754999999999998, 2.9866999999999999, 2.9984999999999999, 3.0109000000000004, 3.0240999999999998, 3.0384000000000002, 3.0542000000000002, 3.0722, 3.0934999999999997, 3.1208999999999998, 3.1621999999999999, NA, NA, 2.3614999999999999, 2.4167000000000001, 2.4632000000000001, 2.5028999999999999, 2.5373999999999999, 2.5678000000000001, 2.5949, 2.6193999999999997, 2.6417000000000002, 2.6620999999999997, 2.6810999999999998, 2.6986999999999997, 2.7153, 2.7309000000000001, 2.7456, 2.7597, 2.7732000000000001, 2.7862, 2.7986999999999997, 2.8108, 2.8226, 2.8341000000000003, 2.8454000000000002, 2.8565, 2.8673999999999999, 2.8783000000000003, 2.8891, 2.8997999999999999, 2.9106999999999998, 2.9216000000000002, 2.9325999999999999, 2.9439000000000002, 2.9554, 2.9674, 2.9798, 2.9927999999999999, 3.0066999999999999, 3.0217999999999998, 3.0384000000000002, 3.0571999999999999, 3.0795000000000003, 3.1080999999999999, 3.1509, NA, NA, NA, 2.3542000000000001, 2.4047000000000001, 2.4481000000000002, 2.4859, 2.5193000000000003, 2.5489999999999999, 2.5758000000000001, 2.6002000000000001, 2.6225000000000001, 2.6431999999999998, 2.6623999999999999, 2.6803999999999997, 2.6972999999999998, 2.7132999999999998, 2.7284999999999999, 2.7431000000000001, 2.7570000000000001, 2.7704999999999997, 2.7835000000000001, 2.7961, 2.8083999999999998, 2.8205, 2.8323, 2.8440000000000003, 2.8555000000000001, 2.867, 2.8784000000000001, 2.8898999999999999, 2.9013999999999998, 2.9131, 2.9249999999999998, 2.9371999999999998, 2.9497, 2.9628000000000001, 2.9765000000000001, 2.9910000000000001, 3.0066999999999999, 3.0240999999999998, 3.0437000000000003, 3.0669, 3.0964999999999998, 3.1408, NA, NA, NA, NA, 2.3486000000000002, 2.3952999999999998, 2.4361999999999999, 2.4723999999999999, 2.5047000000000001, 2.5338000000000003, 2.5602, 2.5844, 2.6068000000000002, 2.6274999999999999, 2.6469, 2.6650999999999998, 2.6824000000000003, 2.6986999999999997, 2.7143000000000002, 2.7292999999999998, 2.7435999999999998, 2.7574999999999998, 2.7709999999999999, 2.7841, 2.7968999999999999, 2.8094999999999999, 2.8219000000000003, 2.8341000000000003, 2.8462000000000001, 2.8582999999999998, 2.8704000000000001, 2.8826000000000001, 2.8949000000000003, 2.9074, 2.9201000000000001, 2.9333, 2.9469000000000003, 2.9613, 2.9765000000000001, 2.9927999999999999, 3.0109000000000004, 3.0312000000000001, 3.0552999999999999, 3.0859000000000001, 3.1315, NA, NA, NA, NA, NA, 2.3441999999999998, 2.3879000000000001, 2.4265999999999996, 2.4614000000000003, 2.4927000000000001, 2.5210999999999997, 2.5472000000000001, 2.5712000000000002, 2.5935999999999999, 2.6143999999999998, 2.6338999999999997, 2.6524000000000001, 2.6699000000000002, 2.6864999999999997, 2.7024999999999997, 2.7178, 2.7326000000000001, 2.7469000000000001, 2.7608000000000001, 2.7744, 2.7877000000000001, 2.8007, 2.8136999999999999, 2.8264, 2.8391999999999999, 2.8518999999999997, 2.8647, 2.8776000000000002, 2.8906999999999998, 2.9039999999999999, 2.9178000000000002, 2.9319999999999999, 2.9469000000000003, 2.9628000000000001, 2.9798, 2.9984999999999999, 3.0196000000000001, 3.0445000000000002, 3.0760999999999998, 3.1230000000000002, NA, NA, NA, NA, NA, NA, 2.3407, 2.3818000000000001, 2.4188000000000001, 2.4523000000000001, 2.4827000000000004, 2.5106000000000002, 2.5362999999999998, 2.5602, 2.5825, 2.6032999999999999, 2.6230000000000002, 2.6417000000000002, 2.6594000000000002, 2.6764000000000001, 2.6925999999999997, 2.7082999999999999, 2.7234000000000003, 2.7382, 2.7524999999999999, 2.7665999999999999, 2.7803, 2.7938999999999998, 2.8074000000000003, 2.8207, 2.8341000000000003, 2.8475000000000001, 2.8609999999999998, 2.8746, 2.8885999999999998, 2.9028999999999998, 2.9178000000000002, 2.9333, 2.9497, 2.9674, 2.9866999999999999, 3.0085999999999999, 3.0341999999999998, 3.0667, 3.1149, NA, NA, NA, NA, NA, NA, NA, 2.3378000000000001, 2.3769, 2.4123000000000001, 2.4447000000000001, 2.4744000000000002, 2.5018000000000002, 2.5271999999999997, 2.5508999999999999, 2.5731000000000002, 2.5940000000000003, 2.6138000000000003, 2.6327000000000003, 2.6505999999999998, 2.6678999999999999, 2.6844000000000001, 2.7004999999999999, 2.7160000000000002, 2.7311000000000001, 2.7458999999999998, 2.7603999999999997, 2.7747000000000002, 2.7888000000000002, 2.8028, 2.8167999999999997, 2.8308, 2.8449, 2.8591000000000002, 2.8736999999999999, 2.8885999999999998, 2.9039999999999999, 2.9201000000000001, 2.9371999999999998, 2.9554, 2.9754999999999998, 2.9980000000000002, 3.0244, 3.0579000000000001, 3.1071999999999997, NA, NA, NA, NA, NA, NA, NA, NA, 2.3355000000000001, 2.3727, 2.4068999999999998, 2.4382999999999999, 2.4672999999999998, 2.4943, 2.5194000000000001, 2.5430000000000001, 2.5651999999999999, 2.5861999999999998, 2.6061000000000001, 2.6251000000000002, 2.6433, 2.6609000000000003, 2.6777000000000002, 2.6940999999999997, 2.71, 2.7256, 2.7408000000000001, 2.7557999999999998, 2.7706, 2.7582, 2.7998000000000003, 2.8144999999999998, 2.8292000000000002, 2.8440000000000003, 2.8591000000000002, 2.8746, 2.8906999999999998, 2.9074, 2.9249999999999998, 2.9439000000000002, 2.9645999999999999, 2.9878, 3.0149999999999997, 3.0492999999999997, 3.0998999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.3334999999999999, 2.3693, 2.4024000000000001, 2.4329999999999998, 2.4614000000000003, 2.488, 2.5129000000000001, 2.5364, 2.5585999999999998, 2.5796000000000001, 2.5996999999999999, 2.6189, 2.6374, 2.6551999999999998, 2.6724000000000001, 2.6890999999999998, 2.7054, 2.7214, 2.7370999999999999, 2.7524999999999999, 2.7679, 2.7831000000000001, 2.7984, 2.8136999999999999, 2.8292000000000002, 2.8449, 2.8609999999999998, 2.8776000000000002, 2.8949000000000003, 2.9131, 2.9325999999999999, 2.9539, 2.9779, 3.0059, 3.0411000000000001, 3.0928, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.3319000000000001, 2.3664000000000001, 2.3984999999999999, 2.4285000000000001, 2.4563999999999999, 2.4827000000000004, 2.5074000000000001, 2.5308000000000002, 2.5529999999999999, 2.5742000000000003, 2.5943999999999998, 2.6138000000000003, 2.6324999999999998, 2.6505999999999998, 2.6681999999999997, 2.6853000000000002, 2.702, 2.7183999999999999, 2.7345999999999999, 2.7505999999999999, 2.7665999999999999, 2.7824, 2.7984, 2.8144999999999998, 2.8308, 2.8475000000000001, 2.8647, 2.8826000000000001, 2.9013999999999998, 2.9216000000000002, 2.9434999999999998, 2.9681999999999999, 2.9969000000000001, 3.0329999999999999, 3.0859000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.3304999999999998, 2.3639999999999999, 2.3952999999999998, 2.4247000000000001, 2.4523000000000001, 2.4782999999999999, 2.5028999999999999, 2.5262000000000002, 2.5484999999999998, 2.5697000000000001, 2.5902000000000003, 2.6097999999999999, 2.6288, 2.6472000000000002, 2.6650999999999998, 2.6825999999999999, 2.6998000000000002, 2.7167000000000003, 2.7334000000000001, 2.75, 2.7665999999999999, 2.7831000000000001, 2.7998000000000003, 2.8167999999999997, 2.8341000000000003, 2.8518999999999997, 2.8704000000000001, 2.8898999999999999, 2.9106999999999998, 2.9333, 2.9585999999999997, 2.9881000000000002, 3.0251000000000001, 3.0792000000000002, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.3292999999999999, 2.3620000000000001, 2.3925999999999998, 2.4215, 2.4487999999999999, 2.4745999999999997, 2.4990999999999999, 2.5225, 2.5448, 2.5661999999999998, 2.5867999999999998, 2.6068000000000002, 2.6260000000000003, 2.6448, 2.6631, 2.6810999999999998, 2.6986999999999997, 2.7161, 2.7334000000000001, 2.7505999999999999, 2.7679, 2.7852000000000001, 2.8028, 2.8207, 2.8391999999999999, 2.8582999999999998, 2.8784000000000001, 2.8997999999999999, 2.9231000000000003, 2.9492000000000003, 2.9795000000000003, 3.0172999999999996, 3.0726, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.3283999999999998, 2.3603000000000001, 2.3904000000000001, 2.4188999999999998, 2.4459, 2.4716, 2.4960999999999998, 2.5194999999999999, 2.5419, 2.5636000000000001, 2.5844, 2.6046, 2.6242000000000001, 2.6434000000000002, 2.6620999999999997, 2.6804999999999999, 2.6986999999999997, 2.7167000000000003, 2.7345999999999999, 2.7524999999999999, 2.7706, 2.7888000000000002, 2.8074000000000003, 2.8264, 2.8462000000000001, 2.867, 2.8891, 2.9129999999999998, 2.9398, 2.9708999999999999, 3.0095999999999998, 3.0661, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.3275999999999999, 2.3588999999999998, 2.3885000000000001, 2.4167000000000001, 2.4436, 2.4691999999999998, 2.4937, 2.5171999999999999, 2.5398000000000001, 2.5617000000000001, 2.5827999999999998, 2.6032999999999999, 2.6233, 2.6429, 2.6620999999999997, 2.6810999999999998, 2.6998000000000002, 2.7183999999999999, 2.7370999999999999, 2.7557999999999998, 2.7747000000000002, 2.7938999999999998, 2.8136999999999999, 2.8341000000000003, 2.8555000000000001, 2.8783000000000003, 2.9028999999999998, 2.9303999999999997, 2.9622999999999999, 3.0019999999999998, 3.0596000000000001, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.3268999999999997, 2.3577000000000004, 2.3870999999999998, 2.415, 2.4417999999999997, 2.4674, 2.492, 2.5156000000000001, 2.5385, 2.5606, 2.5819999999999999, 2.6029, 2.6233, 2.6434000000000002, 2.6631, 2.6825999999999999, 2.702, 2.7214, 2.7408000000000001, 2.7603999999999997, 2.7803, 2.8007, 2.8219000000000003, 2.8440000000000003, 2.8673999999999999, 2.8928000000000003, 2.9210000000000003, 2.9537, 2.9943999999999997, 3.0531999999999999, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.3264, 2.3568000000000002, 2.3859000000000004, 2.4138000000000002, 2.4405000000000001, 2.4661, 2.4908000000000001, 2.5146999999999999, 2.5377999999999998, 2.5602, 2.5819999999999999, 2.6032999999999999, 2.6242000000000001, 2.6448, 2.6650999999999998, 2.6853000000000002, 2.7054, 2.7256, 2.7458999999999998, 2.7665999999999999, 2.7877000000000001, 2.8094999999999999, 2.8323, 2.8565, 2.8826000000000001, 2.9116, 2.9451000000000001, 2.9866999999999999, 3.0468000000000002, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.3260000000000001, 2.3561000000000001, 2.3851, 2.4129, 2.4396, 2.4653999999999998, 2.4903, 2.5143999999999997, 2.5377999999999998, 2.5606, 2.5827999999999998, 2.6046, 2.6260000000000003, 2.6472000000000002, 2.6681999999999997, 2.6890999999999998, 2.71, 2.7311000000000001, 2.7524999999999999, 2.7744, 2.7968999999999999, 2.8205, 2.8454000000000002, 2.8723000000000001, 2.9020999999999999, 2.9364999999999997, 2.9790000000000001, 3.0402999999999998, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, 2.3257000000000003, 2.3555999999999999, 2.3845000000000001, 2.4123000000000001, 2.4392, 2.4651000000000001, 2.4903, 2.5146999999999999, 2.5385, 2.5617000000000001, 2.5844, 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2.5731000000000002, 2.6032999999999999, 2.6338999999999997, 2.6650999999999998, 2.6972999999999998, 2.7309000000000001, 2.7665999999999999, 2.8054999999999999, 2.8494999999999999, 2.9028999999999998, 2.9777), .Dim = c(45L, 30L), .Dimnames = list(c("1", "2", "3", "4", "5", "6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16", "17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27", "28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38", "39", "40", "41", "42", "43", "44", "45"), c("al02", "al04", "al06", "al08", "al10", "al12", "al14", "al16", "al18", "al20", "al22", "al24", "al26", "al28", "al30", "al32", "al34", "al36", "al38", "al40", "al42", "al44", "al46", "al48", "al50", "al52", "al54", "al56", "al58", "al60"))) km.ci/R/bisect.R0000755000176200001440000000063414222644212013055 0ustar liggesusers"bisect" <- function(fun,opar,lval,uval,tol=1e-7) { t1<-fun(lval,opar) t2<-fun(uval,opar) if(t1*t2 > 0 ) stop("in bisect both function values have the same sign") if(t1>0) { t2<-uval uval<-lval lval<-t2 } converged<-FALSE while( !converged ) { t1<-(lval+uval)/2 nf<-fun(t1,opar) if(abs(nf) < tol ) return(t1) else if( nf<0) lval<-t1 else uval<-t1 } } km.ci/R/abweich.nair.fun.R0000755000176200001440000000064313351150552014726 0ustar liggesusers"abweich.nair.fun" <- function(matrix,c) { # Calculates the upper and lower derivation to the Kaplan-Meier estimator # for determining the boundaries of a Hall-Wellner band (which is # symmetric). kap.mei <- matrix[,2] sigma <- matrix[,3] result1 <- c*sqrt(sigma)*kap.mei result2 <- exp((c*sqrt(sigma))/log(kap.mei)) return(list(lin.dev=result1,log.dev=result2)) } km.ci/R/km.ci.R0000755000176200001440000001276314223000316012603 0ustar liggesusers#' Confidence Intervals for the Kaplan-Meier Estimator. #' #' Computes pointwise and simultaneous confidence intervals for the #' Kaplan-Meier estimator. #' #' A simulation study showed, that three confidence intervals produce #' satisfying confidence limits. One is the "loglog" confidence interval, an #' interval which is based on the log of the hazard. The other competitive #' confidence concept was introduced by Rothman (1978) and is using the #' assumption that the survival estimator follows a binomial distribution. #' Another good confidence concept was invented by Thomas and Grunkemeier #' (1975) and is derived by minimizing the likelihood function under certain #' constraints. Special thanks goes to Robert Gentleman for providing code for #' the confidence interval by Thomas and Grunkemeier. #' #' The confidence interval using Peto's variance can not be recommended since #' it yields confidence limits outside the admissible range [0;1] as well as #' the "linear" and the "log" (which is based on the logarithm of S(t)). #' #' The function can produce simultaneous confidence bands, too. The #' Hall-Wellner band (1980) and the Equal Precision band by Nair (1984) #' together with their log-transformed counterpart. From all simultaneous #' confidence intervals only the log-transformed Equal Precision "logep" band #' can be recommended. The limits are computed according to the statistical #' tables in Klein and Moeschberger (2002). #' #' @param survi A survival object for which the new confidence limits should be #' computed. This can be built using the "Surv" and the "survfit" function in #' the R package "survival". "km.ci" modifies the confidence limits in this #' object. #' @param conf.level The level for a two-sided confidence interval on the #' survival curve. Default is 0.95. #' @param tl The lower time boundary for the simultaneous confidence limits. If #' it is missing the smallest event time is used. #' @param tu The upper time boundary for the simultaneous confidence limits. If #' it is missing the largest event time is used. #' @param method One of '"peto"', '"linear"', '"log"', "loglog"', '"rothman"', #' "grunkemeier"', '"hall-wellner"', '"loghall"', "epband"', "logep" #' @return a 'survfit' object; #' #' see the help on 'survfit.object' for details. #' @author Strobl, R. #' @seealso \code{\link[survival]{survfit}}, #' \code{\link[survival]{print.survfit}}, \code{\link[survival]{plot.survfit}}, #' \code{\link[survival]{lines.survfit}}, #' \code{\link[survival]{summary.survfit}}, #' \code{\link[survival]{survfit.object}}, \code{\link[survival]{coxph}}, #' \code{\link[survival]{Surv}}, \code{\link[survival]{strata}}. #' @references Strobl, R., Dirschedl, P. and Mansmann, U.. Comparison of #' simultaneous and pointwise confidence intervals for survival functions. #' (2005, submitted to Biom. J.). #' @keywords survival #' @examples #' #' require(survival) #' data(rectum.dat) #' #' # fit a Kaplan-Meier and plot it #' fit <- survfit(Surv(time, status) ~ 1, data=rectum.dat) #' plot(fit) #' fit2 <- km.ci(fit) #' plot(fit2) #' #' @export km.ci "km.ci" <- function(survi,conf.level=0.95, tl=NA, tu=NA, method="rothman") { # This function can compute the most desirable confidence bands. # The method "log" is implemented as "log" in R survfit. # The method "loglog" is implemented as "log-log" in R survfit. # The method "linear" is called "plain" in R survfit. if(conf.level < 0 || conf.level > 1) stop("confidence level must be between 0 and 1") if (data.class(survi)!="survfit") stop("Survi must be a survival object") method <- match.arg(method,c( "peto", "linear", "log" ,"loglog", "rothman","grunkemeier", "epband", "logep", "hall-wellner","loghall")) if(method=="grunkemeier") { result <- grunk.all.fun(survi,1-conf.level) result$conf.type <- "Grunkemeier" } if(method=="linear") { result <- survi cf <- comp.npci(survi,conf.level) result$lower <- cf$linear$lower result$upper <- cf$linear$upper result$conf.type <- "Linear" } if(method=="rothman") { result <- rothman.fun(survi,conf.level)$surv.object result$conf.type <- "Rothman" } if(method=="peto") { result <- survi cf <- comp.npci(survi,conf.level) result$lower <- cf$peto$lower result$upper <- cf$peto$upper result$conf.type <- "Peto" } if(method=="log") { result <- survi cf <- comp.npci(survi,conf.level) result$lower <- cf$greenwood$lower result$upper <- cf$greenwood$upper result$conf.type <- "Log" } if(method=="loglog") { result <- survi cf <- comp.npci(survi,conf.level) result$lower <- cf$log$lower result$upper <- cf$log$upper result$conf.type <- "Log-Log" } if(method=="hall-wellner") { result <- hall.wellner.fun(survi, tl=tl, tu=tu, conf.lev=conf.level) result$conf.type <- "Hall-Wellner" } if(method=="loghall") { result <- hall.wellner.fun(survi,tl=tl, tu=tu, method="log", conf.lev=conf.level) result$conf.type <- "Log(Hall-Wellner)" } if(method=="epband") { result <- epband.fun(survi, tl=tl, tu=tu, conf.lev=conf.level) result$conf.type <- "Equal Precision" } if(method=="logep") { result <- epband.fun(survi, tl=tl, tu=tu, method="log",conf.lev=conf.level) result$conf.type <- "Log(Equal Precision)" } return(result) } km.ci/R/Expllike.deriv.R0000755000176200001440000000014713351150552014471 0ustar liggesusers"Expllike.deriv" <- function(lambda,times,cens) { d<-sum(cens) return(d/lambda-sum(times)) } km.ci/R/lrt.confints.R0000755000176200001440000000325414222643177014241 0ustar liggesusers#' @importFrom stats qchisq "lrt.confints" <- function(time,status,t0,alpha=0.05) { ftimes<-sort(unique(time[status==1])) k<-length(ftimes) dvec<-rep(1,k) nvec<-dvec jmax<-0 for(i in 1:k) { dvec[i]<-sum(time==ftimes[i] & status==1) nvec[i]<-sum(time>=ftimes[i]) if(t0 >= ftimes[i]) jmax<-i } nsub<-nvec[1:jmax] dsub<-dvec[1:jmax] theta<-qchisq(1-alpha,1) #handle no deaths specially if( jmax == 0 || sum(dsub) == 0 ) return(list(lower=exp(-theta/(2*max(nsub))),upper=1)) #else lrt<-function(lambda,opar) { nsub<-opar$nsub dsub<-opar$dsub opar$theta -2*sum(nsub*log(1+lambda/nsub)-(nsub-dsub)*log(1 + lambda/(nsub-dsub))) } plambda<-function(lambda,opar) { nsub<-opar$nsub dsub<-opar$dsub prod(1-dsub/(nsub+lambda)) } t1<-sum(1/(nsub-dsub)-1/nsub) l1<- -sqrt(theta/t1) #the likelihood is undefined if l1 < lbd lbd<- dvec[jmax]-nvec[jmax] tol2 <- 1/100 #if( nvec[jmax]-dvec[jmax]+l1 < 0 ) { # l1<-(dvec[jmax]-nvec[jmax]-0.001)/10 #} parlist<-list(nsub=nsub,dsub=dsub,theta=theta) for(i in 1:10) { if( l1 < lbd ) { l1<-lbd + tol2 tol2<- tol2/2 } v1 <- lrt(l1,parlist) if(v1 < 0 ) break else { slope<-(theta - v1)/l1 l1<-(theta + 0.5 )/slope } } lower<-bisect(lrt,parlist,l1,0) l1<- -l1 for(i in 1:10) { v1<-lrt(l1,parlist) if(v1 < 0 ) break else { slope<-(theta - v1)/l1 l1<-(theta + 0.5 )/slope } } upper<-bisect(lrt,parlist,0,l1) lp<-plambda(lower,parlist) up<-plambda(upper,parlist) return(list(lower=lp,upper=up)) } km.ci/R/Expllike2.R0000755000176200001440000000016113351150552013437 0ustar liggesusers"Expllike2" <- function(lambda,opar) { d<-sum(opar[[2]]) return(d*log(lambda)-lambda*sum(opar[[1]])) } km.ci/R/hall.wellner.fun.R0000755000176200001440000000673714223000316014764 0ustar liggesusers#' @importFrom utils data "hall.wellner.fun" <- function(survi,tl=NA,tu=NA, method="linear", conf.lev=0.95) { # This function takes a survfit object and modifies it, such that # its lower and upper boundaries are now computed using the # method by Hall-Wellner. # Essentially required are table of critical values, # named "critical.value.hall.90", "critical.value.hall.95" # "critical.value.hall.99" (see also Appendix C # in Klein & Moeschberger p. 451). survi <- survi tl <- tl tu <- tu if(max(conf.lev==c(0.90, 0.95, 0.99))!=1) { stop("confidence level for simultaneous bands must be either 0.90, 0.95 or 0.99") } # if no tl,tu is given the band covers the whole curve if(is.na(tl)&is.na(tu)) { tl <- min(survi$time[survi$n.event>0]) tu <- max(survi$time[survi$n.event>0 &survi$n.risk>survi$n.event]) } n <- survi$n aa <- a.up.low.fun(survi,tl,tu) au <- aa$a.up #determines row in table of critical values al <- aa$a.low #determines column ... dat.mat <- aa$sigma.mat # columns used to interpolate index.al.left <- floor(al/2*100+1) index.al.right <- ceiling(al/2*100+1) # rows ... index.au.top <- floor((au-0.1)/2*100+1) index.au.bottom <- ceiling((au-0.1)/2*100+1) #critical values: readingwise 1. topleft,...,3.bottomleft,... if(conf.lev==0.90) { crit1 <- critical.value.hall.90[index.au.top,index.al.left] crit2 <- critical.value.hall.90[index.au.top,index.al.right] crit3 <- critical.value.hall.90[index.au.bottom,index.al.left] crit4 <- critical.value.hall.90[index.au.bottom,index.al.right] } if(conf.lev==0.95) { crit1 <- critical.value.hall.95[index.au.top,index.al.left] crit2 <- critical.value.hall.95[index.au.top,index.al.right] crit3 <- critical.value.hall.95[index.au.bottom,index.al.left] crit4 <- critical.value.hall.95[index.au.bottom,index.al.right] } if(conf.lev==0.99) { crit1 <- critical.value.hall.99[index.au.top,index.al.left] crit2 <- critical.value.hall.99[index.au.top,index.al.right] crit3 <- critical.value.hall.99[index.au.bottom,index.al.left] crit4 <- critical.value.hall.99[index.au.bottom,index.al.right] } if(is.na(crit2))# just in case { crit2 <- (crit1+crit4)/2 } #percentages of interpolation vert.perc <- 1-(ceiling(au/2*100)-au/2*100) hori.perc <- 1-(ceiling(al/2*100)-al/2*100) #interpolations: numbering clockwise inter1 <- crit1-(abs(crit1-crit2)*hori.perc) inter2 <- crit4-(abs(crit4-crit2)*vert.perc) inter3 <- crit3-(abs(crit3-crit4)*hori.perc) inter4 <- crit3-(abs(crit3-crit1)*vert.perc) interpol <- inter1*(1-vert.perc)+inter4*(1-hori.perc)+inter2*hori.perc+inter3*vert.perc crit <- interpol/2 # First: compute a vector with the deviations devia <- abweich.fun(dat.mat,crit,n) # Now, produce a list with the lower and upper boundary # dependent of the method. if(method=="linear") { up.low.list <- confi.fun(devia$lin.dev,dat.mat[,2],method) } if(method=="log") { up.low.list <- confi.fun(devia$log.dev,dat.mat[,2],method) } # Finally, modify the survfit object with the new boundaries survi$lower <- up.low.list$lower survi$upper <- up.low.list$upper survi <- modify.surv.fun(survi,aa$start,aa$end,method) return(survi) } km.ci/R/epband.fun.R0000755000176200001440000000716114223000316013616 0ustar liggesusers#' @importFrom utils data "epband.fun" <- function(survi, tl=NA,tu=NA, method="linear",conf.lev=0.95) { # This function takes a survfit object and modifies it, such that # its lower and upper boundaries are now computed using the # method by Hall-Wellner. # Essentially required are table of critical values, # named "critical.value.nair.90", "critical.value.nair.95" # "critical.value.nair.99" (see also Appendix C # in Klein & Moeschberger p. 451). survi <- survi tl <- tl tu <- tu if(max(conf.lev==c(0.90, 0.95, 0.99))!=1) { stop("confidence level for simultaneous bands must be either 0.90, 0.95 or 0.99") } # if no tl,tu is given the band covers the whole curve if(is.na(tl)&is.na(tu)) { tl <- min(survi$time[survi$n.event>0]) tu <- max(survi$time[survi$n.event>0 &survi$n.risk>survi$n.event]) } n <- survi$n aa <- a.up.low.fun(survi,tl,tu) au <- aa$a.up #determines row in table of critical values al <- aa$a.low #determines column ... dat.mat <- aa$sigma.mat # columns used to interpolate index.al.left <- floor(al/2*100+1)-1 index.al.right <- ceiling(al/2*100+1)-1 if(index.al.left==0) { index.al.left <- 1 } # rows ... index.au.top <- floor((au-0.1)/2*100+1) index.au.bottom <- ceiling((au-0.1)/2*100+1) if(index.au.bottom==46) { index.au.bottom <- 45 } #critical values: readingwise 1. topleft,...,3.bottomleft,... if(conf.lev==0.90) { crit1 <- critical.value.nair.90[index.au.top,index.al.left] crit2 <- critical.value.nair.90[index.au.top,index.al.right] crit3 <- critical.value.nair.90[index.au.bottom,index.al.left] crit4 <- critical.value.nair.90[index.au.bottom,index.al.right] } if(conf.lev==0.95) { crit1 <- critical.value.nair.95[index.au.top,index.al.left] crit2 <- critical.value.nair.95[index.au.top,index.al.right] crit3 <- critical.value.nair.95[index.au.bottom,index.al.left] crit4 <- critical.value.nair.95[index.au.bottom,index.al.right] } if(conf.lev==0.99) { crit1 <- critical.value.nair.99[index.au.top,index.al.left] crit2 <- critical.value.nair.99[index.au.top,index.al.right] crit3 <- critical.value.nair.99[index.au.bottom,index.al.left] crit4 <- critical.value.nair.99[index.au.bottom,index.al.right] } if(is.na(crit2))# just in case { crit2 <- (crit1+crit4)/2 } #percentages of interpolation vert.perc <- 1-(ceiling(au/2*100)-au/2*100) hori.perc <- 1-(ceiling(al/2*100)-al/2*100) #interpolations: numbering clockwise inter1 <- crit1-(abs(crit1-crit2)*hori.perc) inter2 <- crit4-(abs(crit4-crit2)*vert.perc) inter3 <- crit3-(abs(crit3-crit4)*hori.perc) inter4 <- crit3-(abs(crit3-crit1)*vert.perc) interpol <- inter1*(1-vert.perc)+inter4*(1-hori.perc)+inter2*hori.perc+inter3*vert.perc crit <- interpol/2 # First: compute a vector with the deviations devia <- abweich.nair.fun(dat.mat,crit) # Now, produce a list with the lower and upper boundary # dependent of the method. if(method=="linear") { up.low.list <- confi.nair.fun(devia$lin.dev,dat.mat[,2],method) } if(method=="log") { up.low.list <- confi.nair.fun(devia$log.dev,dat.mat[,2],method) } # Finally, modify the survfit object with the new boundaries survi$lower <- up.low.list$lower survi$upper <- up.low.list$upper survi <- modify.surv.fun(survi,aa$start,aa$end,method) return(survi) } km.ci/R/Expllike.R0000755000176200001440000000015513351150552013360 0ustar liggesusers"Expllike" <- function(lambda,times,cens) { d<-sum(cens) return(d*log(lambda)-lambda*sum(times)) } km.ci/R/confi.fun.R0000755000176200001440000000075414222644312013475 0ustar liggesusers"confi.fun" <- function(abw,kap.mei,method) { # Using the already calculated derivation this function calculates # the upper and lower boundary of a confidence band by substracting # resp. adding the derivation "abw". if(method=="linear") { lower <- kap.mei-abw upper <- kap.mei+abw } if(method=="log") { lower <- kap.mei^(1/abw) upper <- kap.mei^abw } return(list(lower=lower, upper=upper)) } km.ci/R/confi.nair.fun.R0000755000176200001440000000076013351150552014422 0ustar liggesusers"confi.nair.fun" <- function(abw,kap.mei,method) { # Using the already calculated derivation this function calculates # the upper and lower boundary of a confidence band by substracting # resp. adding the derivation "abw". if(method=="linear") { lower <- kap.mei-abw upper <- kap.mei+abw } if(method=="log") { lower <- kap.mei^(1/abw) upper <- kap.mei^abw } return(list(lower=lower,upper=upper)) } km.ci/MD50000644000176200001440000000321314223277412011566 0ustar liggesusers72d24ef9d06d67bad9a709e964265db3 *DESCRIPTION a7aaba5e0079e4548f5e52435e18cfc6 *NAMESPACE 62397d78aa7ecff1529cced87b4bf7be *R/Expllike.R 82d593d4c9d9082cf0e687edd01508be *R/Expllike.deriv.R 07451fe384c78a0eaaeca987e097e322 *R/Expllike2.R 191fa19a48b86a951f38adbf3612cf06 *R/a.up.low.fun.R 49b7bcf9b3f8e4457b7f6d4b3429ed89 *R/abweich.fun.R 027851b24a554fc04477e2afeab0111e *R/abweich.nair.fun.R 30d17b412b9bcbec3af5dadb6b4f74d3 *R/bisect.R 2605c555cd86b2386b08ccc5dabef9fc *R/comp.npci.R a5680ec96a48413add544a5abf0c9530 *R/confi.fun.R cbfca4346726c57f74a27c6d584fecf0 *R/confi.nair.fun.R 6c8d1523101231468feccccd10ba1e8a *R/critical.value.R 0f06a461f1e3c59f5e64275639e4185f *R/epband.fun.R 954bada3b9dad9434f9bc8490d8dbe24 *R/globals.R 2802d4bf7b6fd4250489b0d0cdf2ea27 *R/grunk.all.fun.R 6ea278c031311487151f1f5d2b02ed48 *R/hall.wellner.fun.R 97ebb0c10d7b9b63b6bd7d43bb78cc97 *R/km.ci-package.R 92bef832e3e9582a2a29f94461f55619 *R/km.ci.R 0d7f63f16bbe0d193c9cc99abbb95ce3 *R/lrt.confints.R 58c151571302b1fc7c0f6e72144194d5 *R/modify.surv.fun.R 286d200491629211025f5f1c83e20416 *R/rothman.fun.R 4210b71c14b1ae6b5360b4ec14c6af49 *data/rectum.dat.rda 20b61df788820264d1aea9c29a80bf9b *inst/NEWS 0aa39d9e4d39af1d6704cf3bf450ed48 *man/critical.value.hall.90.Rd 425c95d219bd821ef46e2bf2c3215a5e *man/critical.value.hall.95.Rd 0f9e0e878aa7458d91d9e10241f6fede *man/critical.value.hall.99.Rd e508c3026321a8213fa8e4ec271e9c22 *man/critical.value.nair.90.Rd 38a88e3a9dc5904cfe97e493e7ad8fa0 *man/critical.value.nair.95.Rd b54fb5825e4b6934fc949c1ba120aabb *man/critical.value.nair.99.Rd 1f85648f16f26270e6eb0c6672cbcc9a *man/km.ci.Rd d7ff9ac6c8f7116c27f20324730d2e33 *man/rectum.dat.Rd km.ci/inst/0000755000176200001440000000000014223000316012217 5ustar liggesuserskm.ci/inst/NEWS0000644000176200001440000000055014223001016012714 0ustar liggesusers0.5-6 o define built-in lookup tables critical.value.hall.90, critical.value.hall.95, critical.value.hall.99, critical.value.nair.90, critical.value.nair.95 and critical.value.nair.99 in R/critical.value.R and export o move help pages to roxygen2 o miscellaneous fixes to comply with R package checker 0.5-3 o fix in epband.fun by Ed Claassens